UNIVERSITY  OF  CALIFORNI 
LOS  ANGELES 


WIRE  ROPES. 


ALBERT 


M.  E. 


CADET-ENGINEER  U.  S.  N. 


NEW   YORK: 

D.  VAN  NOSTRAND,  PUBLISHER, 
23  MURRAY  AND  27  WARREN  STREET. 

1877. 

1  2  4 


TT 
IMS' 

57  ft 


PREFACE. 


It  has  been  my  object,  in  the  prepara- 
tion of  {his  work,  to  make  it  a  complete 
exposition  of  the  theory  and  practice  of 
transmitting  power  by  wire  ropes. 

No  complete  treatise  on  this  subject 
has  yet  been  published  in  the  English 
language,  although  the  practical  part  of 
the  matter  is  well  explained  by  the  U.  S. 
Commissioners  in  their  report  on  the 
Paris  Exposition  of  1867,  and  by  an  ex- 
cellent pamphlet  written  by  W.  A. 
Roebling,  C.  E.,  to  which  I  am  indebted 
for  much  practical  information. 

In  Europe,  this  method  of  transmitting 
power  has  found  many  ardent  supporters. 
Among  them,  I  may  mention  Prof.  F. 
Reuleaux  of  Berlin,  ^ho  has  devoted  a 
number  of  chapters  to  it  in  his  various 
scientific  publications,  and  Messrs.  J.  J. 

463267 


Rieter  &  Co.  of  Winterthur,  Switzerland. 
The  latter  gentlemen  have  erected  by 
far  the  greatest  number  of  transmissions 
there;  and  their  engineer,  Mr.  D.  H. 
Ziegler,  has  written  quite  extensively  on 
the  matter. 

In  this  country  the  John  A.  Roebling's 
Sons  Co.  are  the  largest  manufacturers. 

It  is  to  the  publications  above  men- 
tioned, that  much  of  the  matter  in  the 
following  pages  is  due. 


TRANSMISSION  OF  POWER 
BY  WIRE  ROPES. 


SECTION  I. 

INTRODUCTION. 

IT  is  a  noteworthy  historical  fact,  that 
economy  in  the  generation  of  power  in 
the  motor,  and  economy  in  its  utilization 
in  the  machine,  have,  in  most  countries, 
been  far  in  advance  of  its  economical 
transmission  from  the  one  to  the  other. 

Ever  since  the  steam  engine  became 
an  established  fact  in  the  hands  of  Watt, 
inventors  have  been  engaged  in  making 
improvements  to  render  it  still  more  effi- 
cient. The  immense  strides  taken  in  ad- 
vance may  be  well  appreciated  by  even 
the  most  casual  comparison  of  the  en- 
gine of  Watt's  time,  with  one  of  the 


powerful  and  economical  engines  of  the 
present  day. 

Not  only  have  such  ideas,  as  the  ex- 
pansion of  steam,  been  developed  to  a 
remarkable  extent,  but  even  in  the  small- 
est details  the  watchful  eye  of  the  me- 
chanic has  ever  been  finding  room  for 
improvement. 

In  the  course  of  invention,  the  prin- 
ciples upon  which  the  steam  engine  has 
been  made  a  practical  success  have  been 
developed;  and  during  the  present  cen- 
tury, the  chief  application  of  inventive 
genius  has  been  turned  in  the  direction 
of  improvement  in  the  combination  of 
the  parts  of  the  engine  itself.  There  has 
been  no  fundamental  change  in  the  con- 
ception of  the  necessary  parts  of  the 
steam  engine;  but  various  modifications 
of  the  mechanism  have  been  introduced, 
whereby  the  power  has  been  economized, 
or  the  necessary  friction  of  the  parts  has 
been  lessened.  Influenced  by  the  same 
spirit  which  has  characterized  the  scien- 
tific advance  of  this  century;  by  the  in- 
creasing necessity  of  more  accurate 


methods;  and  forced  by  the  industrial 
competition  of  the  age  to  consider  the 
importance  of  economy  of  time  and  en- 
ergy, the  improvers  of  the  steam  engine 
have  seen  that  their  inventions  would 
be  recognized  as  valuable,  only  as  they 
attained  the  same  results  with  increased 
simplicity  of  action,  with  less  waste  of 
power  in  the  working  of  the  mechanism, 
or  with  a  less  supply  of  fuel. 

As  the  Englishman,  Watt,  in  the  last 
century,  found  the  steam  engine  an  im- 
perfect and  wasteful  arrangement  for 
utilizing  only  a  small  portion  of  the  en- 
ergy of  the  steam  supplied  to  it,  and  by 
his  invention  of  a  separate  condenser, 
and  then  by  his  method  of  making  the 
engine  double-acting,  made  it  really  a 
steam  engine;  so  in  this  century  the 
credit  is  largely  due  to  Americans,  such 
as  Allen,  Corliss  and  others,  for  improve- 
ments by  which,  in  the  engines  known 
under  their  respective  names,  simplicity 
of  construction,  together  with  perfection 
of  economy  in  working,  have  been  se- 
cured. 


While,  in  the  department  of  steam 
engineering,  as  well  as  in  the  no  less  im- 
portant domain  of  boiler-making,  we  are 
thus  devoting  all  our  energies  to  increas- 
ing the  efficiency  of  the  prime  mover,  a 
painful  lack  of  care  is  manifest  in  the 
utilization  of  the  power  which  we  pur- 
chased so  dearly.  Obtaining  only  a 
small  fraction  of  the  theoretical  power, 
it  becomes  us  to  husband  it  with  the 
greatest  care,  and  to  allow  it  to  do  its 
allotted  work  with  the  least  possible 
waste  in  the  transmission  from  the  prime 
mover  to  the  machine. 

Years  ago  there  were  excellent  water- 
wheels,  and  by  them  were  driven  ma- 
chines of  surprising  ingenuity,  but  the 
power  was  conveyed  to  the  machines  by 
means  of  cumbersome  wooden  shafts, 
upon  which  were  wooden  drums  for  the 
driving  belts;  gearing,  too,  made  of 
wood;  slow-moving,  awkward  contriv- 
ances for  the  purpose,  and  very  wasteful 
of  power.  In  Oliver  Evans'  "Mill- 
wright's Guide,"  which  is  recognized  as 
the  standard  book  of  his  time,  we  read 


9 

of  wooden  shafts,  wooden  drums,  and 
wooden  gearing  only. 

At  a  later  day,  gear  wheels  were  used 
to  transmit  the  power  from  the  motor 
to  the  shaft,  while  belts  or  bands  were 
only  used  to  transmit  the  power  from 
the  shafts  to  the  individual  machines. 

The  transmission  of  power  to  distances 
was  accomplished  by  lines  of  shafting, 
either  laid  in  ditches  underground,  or 
supported  on  columns  high  enough  not 
to  impede  passage  beneath  the  shafts. 
But  even  this  method  was  seldom  used, 
except  in"  cases  of  necessity,  owing  to  its 
immense  first  cost. 

Although  among  the  most  efficient 
means  of  transmitting  power  to  short 
distances,  both  belting  and  shafting  have 
the  disadvantage,  that  when  the  distance 
becomes  great,  the  intermediate  mechan- 
ism absorbs  an  important  portion  of  the 
power  by  vibrations,  friction,  and  resist- 
ances of  every  nature ;  and,  for  a  distance 
of  several  hundred  feet,  we  do  not  get, 
at  one  end  of  the  transmission,  more 
than  an  extremely  small  fraction  of  the 
power  applied  to  the  other. 


10 

In  the  case  of  a  mere  dead  pull,  as  in 
working  a  pump,  work  is,  and  has  long 
been,  transmitted  to  great  distances;  as 
by  the  long  lines  of  "  draw-rods,"  used 
in  mining  regions  to  transmit  the  power 
of  a  water-wheel  by  means  of  a  crank 
on  its  main  axis,  pulling,  during  half  its 
revolution,  against  a  heavy  weight,  and 
thus  storing  up  energy  for  the  return 
stroke,  as  the  rods,  on  account  of  their 
flexibility,  cannot  be  used  to  exert  a 
pushing  strain.  Rotary  motion,  how- 
ever, cannot  be  economically  produced  in 
this  manner. 

Another  method,  which  has  been  much 
employed  recently,  is  that  known  as  hy- 
draulic connection;  and  Armstrong  has 
even  perfected  apparatus  by  which  water 
pressure,  thus  transmitted  through,  per- 
haps, miles  of  pipe,  may  be  converted 
into  rotary  motion. 

Compressed  air  has  also  come  largely 
into  use,  and  there  ig  no  doubt  that 
power  may  be  transmitted  to  great  dis- 
tances by  rarefied  or  compressed  air,  and 
may  be  converted  into  rotary  motion  at 


11 

any  desired  point.  But  in  the  compres- 
sion of  air,  heat  is  generated;  and  the 
latter  being  conducted  rapidly  away  by 
the  sides  of  the  tube,  the  loss  from  this 
source  alone  becomes  very  serious.  An- 
other disadvantage,  incident  on  both  of 
the  last  two  cases,  is  that  unless  the  area 
of  the  tubes  is  very  large  compared  with 
the  current  flowing  through  them,  the 
loss  by  friction  rises  to  a  large  percent- 
age of  the  power  transmitted.  The 
capital  to  be  sunk  in  pipes,  therefore,  is 
very  large,  and  both  this  expenditure 
and  the  waste  of  power  increase  directly 
with  the  distance. 

Such  were  some  of  the  methods  em- 
ployed to  transmit  power  to  great  dis- 
tances, before  the  invention  of  trans- 
mission of  power  by  wire  ropes  by  the 
Brothers  Hirn,  of  Mulhausen,  Switzer- 
land.* These  gentlemen  have  stated  the 
question  of  the  transmission  of  power  in 
the  most  general  manner,  i.  e.,  independ- 
ently of  the  intensity  of  the  pressure  to  be 

*  See  "  Notice  sur  la  transmission  telodynamique,  par 
C.  F.  Hirn  (Colmar,  1862)." 


12 

* 

transmitted,  and  of  the  distance  to  be 
passed  over;  and  the  solution  which  they 
have  given  to  this  grand  problem  is  so  sim- 
ple, that  the  apparatus  proposed  seems, 
to  the  casual  observer,  to  be  little  else 
than  a  more  extended  application  of  that 
commonplace  "  wrapping  connector,"  the 
belt  and  pulley.  The  principle  involved, 
however,  is  something  entirely  different. 

Simplicity,  always  the  fundamental 
characteristic  of  great  inventions,  rarely 
shows  itself  more  clearly  than  in,  as  they 
are  called,  the  telodynamic  cables.  To 
a  person  seeing  them  in  operation,  they 
seem  the  embodiment  of  simplicity; 
nevertheless,  the  Brothers  Him  have  the 
undisputed  honor  of  inventing  them. 
To  satisfy  themselves  on  this  point,  the 
International  Jury  at  the  Paris  Exposi- 
tion in  1867  made  a  deep  research,  and 
examined  the  patent  registers  for  many 
years  back,  but  failed  to  find  anything 
bearing  the  least  resemblance  to  the 
telodynamic  cables. 

This  method  of  transmitting  power 
depends  upon  two  principles  in  mechan- 


*  13 

(1)  The  dynamic  force  is  measured  by 
the  product  of  the  force  and  the  veloci- 
ty with  which  it  moves ; 

(2)  In  mechanical  work,  power  may 
be  exchanged  for  velocity,  and  velocity 
for  power. 

To  illustrate,  let  us  suppose  a  bar  of  iron, 
having  a  cross  sectional  area  of  one  square 
inch,  to  move  endlong  at  the  rate  of  two 
feet  per  second.  Now,  if  the  resistance 
overcome  is  say  5,000  pounds,  work  will 
be  performed  at  the  rate  of  10,000  foot- 
pounds per  second.  Now,  if  we  double 
the  velocity  of  the  bar,  we  will  transmit 
twice  the  amount  of  work  with  the  same 
strain,  or  the  same  work  may  be  pro- 
duced with  only  half  the  former  strain, 
i.e.,  by  a  bar  having  an  area  of  only  half 
a  square  inch.  In  a  similar  manner,  if 
we  move  the  bar  with  the  velocity  em- 
ployed in  telodynamic  transmission,  viz., 
about  eighty  feet  per  second,  then,  while 
doing  the  same  amount  of  work,  the 
strain  on  the  bar  will  be  reduced  from 
5000  to  125  pounds,  and  the  bar  will  only 
need  a  section  of  1-40  square  inch.  To 


14 

put  an  extreme  illustration,  we  might 
conceive  of  a  speed  at  which  an  iron 
wire,  as  fine  as  a  human  hair,  would  be 
able  to  transmit  the  same  amount  of 
work  as  the  original  one-inch  bar. 

By  the  application  of  these  simple 
principles  in  Hirn's  apparatus,  the  greater 
part  of  the  force  is  first  converted  into 
velocity,  and  at  the  place  where  the 
power  is  required,  the  velocity  is  changed 
back  into  force. 

SECTION  II. 

THE    DRIVING   WHEELS. 

The  construction  of  the  apparatus  is 
very  simple.  A  tolerably  large  iron 
wheel,  having  a  V  shaped  groove  in  its 
rim,  is  connected  with  the  motor,  and 
driven  with  a  perimetral  velocity  of  from 
sixty  to  one  hundred  feet. 

Round  this  wheel  is  passed  a  thin  wire 
rope,  which  is  led  away  to  almost  any 
reasonable  distance  (the  limit  being 
measurable  by  miles),  where  it  passes 
over  a  similar  wheel,  and  then  returns 


15 


as  an  endless  band  to  the  wheel  whence 
it  started. 

The  peripheries  of  the  driving  wheels 
may  have  an  angular  velocity  as  great 
as  possible ;  the  only  limit,  in  fact,  being 
that  the  speed  shall  not  be  likely  to 
destroy  the  wheels  by  centrifugal  force. 
The  speeds  which  have  been  actually 
employed  in  the  examples  to  which  I 
propose  to  refer,  vary  from  25  to  100 
feet  per  second,  at  the  circumference  of 
the  pulley. 

The  wheels  themselves  are  made  as 
light  as  is  consistent  with  strength,  not 
only  for  the  sake  of  reducing  the  inertia 
of  the  moving  mass,  and  the  friction  on 
the  axis  to  a  minimum,  but  for  the  equal- 
ly important  object  of  diminishing  the 
resistance  of  the  air.  It  can  hardly  be 
doubted  that  abandoning  spokes  en- 
tirely, and  making  the  pulley  a  plain 
disc,  would  improve  essentially  the.  per- 
formance, could  such  discs  be  made  at 
once  strong  enough  to  fulfill  the  required 
function,  and  light  enough  not  material- 
ly to  increase  the  friction. 


Fig.. 


17 

The  wheels  have  been  made  of  cast 
iron  and  steel,  and  beside  their  lightness,, 
have  but  one  peculiarity  of  construction,, 
and  that  is  a  highly  important  one.  At 
the  bottom  of  the  acute  V  shaped  groove,, 
going  around  the  circumference,  a  little 
trough  is  formed  in  which  the  filling  is- 
placed,  as  shown  in  Fig.  1. 

The  materials  used  for  this  filling  are 
many  in  number,  and  will  be  discussed 
further  on.  The  rope  should  always  run 
on  a  filling  of  some  kind,  and  not  direct- 
ly on  the  iron,  which  would  quickly  wear 
it  out. 

The  rope  is  not  tightly  stretched  over 
the  wheels,  but,  to  all  appearances,  hangs 
loosely  on  the  same.  But  the  rope 
does  not  slip,  as  the  tension  caused  by 
its  own  weight  presses  it  hard  againt  the 
rims  of  the  wheels,  if  the  latter  are  of 
proper  size.  The  body  of  the  driving 
wheel  differs  very  little  from  that  of  a 
belt  pulley;  and  it  can  always  be  propor- 
tioned as  a  belt  pulley  having  to  trans- 
mit the  same  power  with  the  same  velo- 
city. The  peculiarity  of  the  wheel  lies 


in  its  rim,  as  previously  explained.  In 
the  early  experiments  on  the  transmission 
of  power  in  this  manner,  the  rims  were 
made  of  wood  with  a  leather  belt  as  fill- 
ing, (see  Figs.  2  and  3). 

Fig-3 


This  kind  of  rim  has  now  gone  entirely 
out  of  use,  and  has  been  replaced  by  a 


19 


wheel  cast  solid  with  an  iron  rim,  whose 
edges,  in  a  a  single  grooved  wheel,  are 
inclined  at  about  twenty-five  degrees 
from  the  vertical,  (Figs.  1  and  4).  In 
some  instances  where  the  ropes  were  ex- 
posed to  a  high  side  wind,  the  slope  has 
been  made  as  great  as  45°,  but  this  a 
very  unusual  case. 


The  angle  of  30°,  if  used  in  a  double 
grooved  wheel,  would  give  an  extremely 


20 

heavy  central  rib,  on  which  account  the 
sides  of  the  latter  are  usually  made 
steeper,  viz.,  about  15°  from  the  vertical. 
Wheels  from  about  nine  feet  in  diameter 
up  are  usually  cast  in  halves  and  after- 
ward fastened  together  on  the  shaft.  In 
order  that  the  centrifugal  force  may  not 
become  dangerous,  the  perimetral  veloci- 
ty should  not  exceed  90  to  100  feet  per 
second.  Velocities  up  to  90  feet  have 
been  frequently  used,  without  any  preju- 
dicial results  whatever. 

SECTION  III. 

THE    DRIVING   ROPES. 

The  driving  rope  usually  employed  in 
this  country  consists  of  six  strands,  with 
seven  wires  to  each  strand  (see  Fig.  5). 
The  strands  are  spun  around  a  hempen 
center  or  core,  thus  obtaining  the  neces- 
sary flexibility. 

When  wire  rope  is  referred  to  in  this 
thesis  without  special  qualification,  it  is 
to  be  understood  to  mean  Messrs.  J.  A. 
Roebling's  Sons'  42  wired  round  iron 


21 


wire  rope.  The  diameter  of  this  kind  of 
rope  is  nine  times  the  diameter  of  the 
wire  of  which  it  is  composed.  That  is 
to  say,  if  D  =  the  diameter  of  the  rope, 
and  d  =  diameter  of  the  wire,  then  D 


The  following  table  gives  the  weight, 
strength,  etc.,  of  Messrs.  Roebling's 


22     - 

42    WIKED    ROPE  I 


s 

o 
o 

1 

to 

i   io 

,c 

e* 

s  • 

«M 

S  ro 

•a  o5  1  g 

s 
5 

1 

ameter  ii 
inches. 

rcu  in  fere 
in  inches 

1.1 

il 

a  .5 

imatestr< 
n  pound 

oper  ten* 
n  pound 

*oJ 

si 

a£ 
a  « 

SJ  0 

t£ 

5 

o 

5 

£ 

£'^ 

25 

1 

i 

.125 

2060 

515 

5 

24 

£  r 

.162 

2760 

690 

7 

23 

22 

1 

11 

.189 
.23 

3300 
4260 

825 
1065 

8 
9 

21 

H 

.3 

5660 

1415 

10 

20 

^. 

if 

.41 

8200 

2050 

12 

19 

1 

.5 

11600 

2900 

14 

18 

ii 

2J 

.686 

15200 

3800 

17 

17 

£ 

2f 

.86 

17600 

4400 

20 

16 

-I 

2| 

1.12 

24600 

6150   25 

15 

1 

3 

1.43 

32000 

8000 

32 

In  the  manafacture  of  the  rope,  the 
quality  of  the  iron  wire  must  be  inspect- 
ed very  carefully,  in  order  to  insure  du- 
rability. The  best  wire  is  that  made  of 
Swedish  iron,  uniting  great  toughness 
with  great  tensile  strength.  Steel  wire 
has  not  been  found  well  adapted  for  this 
work.  Particular  attention  must  be  paid 
to  getting  each  wire  as  long  as  possible, 
so  as  to  lessen  the  number  of  joints. 


23 

In  splicing  a  wire  rope,  the  greatest 
care  must  be  taken  to  leave  no  projecting 
ends  or  thick  parts  in  the  rope.  On  this 
subject,  I  can  do  no  better  than  give 
Messrs.  Roebling's  directions  for  making 
a  long  splice  in  an  endless  running  rope 
of  half  inch  diameter.* 

Tools  required:  One  pair  of  nippers, 
for  cutting  off  ends  of  strands;  a  pair  of 
pliers,  to  pull  through  and  straighten 
ends  of  strands;  a  point,  to  open  strands; 
a  knife,  for  cutting  the  core;  and  two 
rope  nippers,  with  sticks  to  untwist  the 
rope;  also  a  wooden  mallet. 

First. — Heave  the  two  ends  taut,  with 
block  and  fall,  until  they  overlap  each 
other  about  twenty  feet.  Next,  open 
the  strands  of  both  ends  of  the  rope  for 
a  distance  of  ten  feet  each;  cut  off  both 
hemp  cores  as  closely  as  possible  (see 
Fig.  6),  and  then  bring  the  open 
bunches  of  strands  face  to  face,  so  that 
the  opposite  strands  interlock  regularly 
with  each  other. 

*  See  "  Transmission  of  Power  by  Wire  Ropes,"  by  W. 
A.  Roebling,  C.  E. 


24 

Secondly. — Unlay  any  strand,  a,  and 
follow  up  with  the  strand  1  of  the  other 
end,  laying  it  tightly  into  the  open 
groove  left  upon  unwinding  a,  and  mak- 
ing the  twist  of  the  strand  agree  exactly 
with  the  lay  of  the  open  groove,  until 
all  but  about  six  inches  of  1  are  laid  in, 
and  a  has  become  twenty  feet  long. 
Next  cut  off  a  within  six  inches  of  the 
rope  (see  Fig.  7),  leaving  two  short  ends, 
which  must  be  tied  temporarily. 

Thirdly. — Unlay  a  strand,  4,  of  the 
opposite  end,  and  follow  up  with  the 
strand,  /",  laying  it  into  the  open  groove, 
as  before,  and  treating  it  precisely  as  in 
the  first  case  (see  Fig.  8).  Next,  pursue 
the  same  course  with  b  and  2,  stopping, 
however,  within  four  feet  of  the  first  set; 
next  with  e  and  5;  also  with  c,  3  and 
rf,  4.  We  now  have  the  strands  all  laid 
into  each  other's' places,  with  the  respect- 
ive ends  passing  each  other  at  points 
four  feet  apart,  as  shown  in  Fig.  9. 

Fourthly. — These  ends  must  now  be 
secured  and  disposed  of,  without  increas- 
ing the  diameter  of  the  rope,  in  the  fol- 


25 


26 

lowing  manner:  Nipper  two  rope- si  ings 
around  the  wire  rope,  say  six  inches  on 
each  side  of  the  crossing  point  of  two 
strands.  Insert  a  stick  through  the  loop 
and  twist  them  in  opposite  directions, 
thus  opening  the  lay  of  the  rope  (see 
Fig.  10).  Now  cut  out  the  core  for  six 
inches  on  the  left  and  stick  the  end  of  1 
under  a,  into  the  place  occupied  by  the 
core.  Next,  cut  out  the  core  in  the  same 
way  on  the  right,  and  stick  the  end  of  a 
in  the  place  of  the  core.  The  ends  of 
the  strands  must  be  straightened  before 
they  are  stuck  in. 

Now  loosen  the  rope  nipper  and  let 
the  wire  rope  close.  Any  slight  inequal- 
ity can  be  taken  out  by  pounding  the 
rope  with  a  wooden  mallet. 

Next,  shift  the  rope  nippers,  and  re- 
peat the  operations  at  the  other  five 
places. 

After  the  rope  has  run  for  a  day,  the 
locality  of  the  splice  can  be  no  longer 
detected.  There  are  no  ends  turned 
under  or  sticking  out,  as  in  ordinary 
splices,  and  the  rope  is  not  increased 


27 

in  size,  nor  appreciably  weakened  in 
strength. 

I  have  dwelt  so  minutely  on  the  pro- 
cess of  splicing,  because  practical  ex- 
perience has  demonstrated  that  a  man 
who  can  splice  a  wire  rope  well,  is  some- 
thing of  a  rarity.  Some  of  the  best 
ship-riggers  are  utterly  non-plussed  when 
a  wire  rope  is  presented  to  them  to  be 
spliced;  and  the  splice  they  produce  is 
usually  half  again  as  thick  as  the  rope, 
and  utterly  useless  for  the  intended  pur- 
pose. 

When  a  rope  has  been  well  spliced  and 
kept  running,  its  average  life  is  about 
three  years. 

Up  to  this  point,  I  have  been  speaking 
of  the  common  wire  ropes,  as  generally 
made  and  used  for  the  purpose  of  trans- 
mitting power,  viz.,  wire  ropes  with 
hemp  centers,  and  also  those  with  wire 
centers.  The  latter  have  not  given  sat- 
isfactory results,  as  they  wear  out  very 
rapidly.  The  only  advantages  to  be 
gained  by  using  a  wire  center  rattier 
than  one  of  hemp,  are  that  the  same 


28 

amount  of  force  may  be  transmitted  with 
a  relatively  smaller  rope,  and  that  the 
rope  itself  stretches  less.  This  latter 
difficulty  can  be  almost  entirely  obviated, 
as  will  be  explained  further  on;  and  as 
the  ropes  with  hemp  centers  are  much 
more  durable,  they  are  now  the  only 
ones  used.  Another  disadvantage  found 
in  the  use  of  ropes  with  wire  centers,  is 
that  the  splice  must  be  made  nearly 
twice  as  long  as  when  hemp  is  used  for 
the  center.  This  must  be  done  to  pre- 
vent the  two  ends  of  the  ^rope  from 
slipping  out,  as  the  co-efficient  of  friction 
is  not  so  great  between  iron  and  iron,  as 
between  iron  and  hemp. 

As  in  splicing,  the  wire  center  is  cut 
off  at  the  splice,  and  not  spliced  in,  it  is 
free  to  move  in  the  rope  in  the  direction 
of  least  resistance.  It  consequently  hap- 
pens that  the  wire  center  frequently  pro- 
trudes through  the  strands  of  the  rope. 
This  may  be  partly  remedied  by  sewing 
with  cord  through  the  center  and  the 
outside  wires,  thus  fastening  them  in  their 
proper  relative  positions.  In  a  short 


29 

time,  however,  the  center  will  again  pro- 
ject; we  are  then  compelled  to  cut  off 
the  projecting  end,  and  repeat  the  opera- 
tion of  sewing  with  cord;  which  does 
not  by  any  means  improve  the  durability 
of  the  rope.  The  principal  difficulty, 
the  excessive  wear  of  the  outer  wires,  is 
common  to  both  kinds  of  ropes.  This 
wear  is  caused  chiefly  by  the  friction  of 
the  wire  on  the  sides  of  the  wheel-groove, 
when  the  rope,  for  any  reason,  runs  un- 
steadily and  swings  against  the  sides  of 
the  groove.  The  ropes  get  flat  in 
places  and  finally  the  wires  break. 

We  may  keep  a  transmission  in  as 
thorough  repair  as  we  will,  but  we  can 
not  prevent,  that  at  times  there  will  be 
more  or  less  oscillating  and  swinging  of 
the  ropes  against  the  wheel-rim,  result- 
ing in  the  wear  above  referred  to.  This 
evil  may  be  greatly  obviated  by  making 
the  section  of  the  wheel-rim  more  of  the 
form  shown  in  Fig.  1 1.  But  this  is  at- 
tended with  several  disadvantages,  par- 
ticularly in  the  case  of  double-grooved 
wheels  (compare  Figs.  12  and  13). 


This  would  increase  the  difficulty  and 
expense  of  making  the  wheels,  and  would 
have  the  great  disadvantage  that  the  dis- 
tance between  the  ropes  would  be  great- 


31 


er,  resulting  in  a  considerable  side  press- 
ure on  the  bearings  of  the  shafts. 


To  prevent  the  wear  of  the  wires,  and 
thus  to  make  the  ropes  more  durable, 
has  been  the  object  of  several  inven- 
tions ;  all  of  which  were  attempts  at  sur- 
rounding the  wires  with  a  flexible  and 
durable  covering,  protecting  the  wires, 
and  at  the  same  time  not  increasing  the 
difficulties  of  splicing.  It  was  also 
thought,  that  if  this  could  be  made  a 
practical  success,  the  filling  in  the  wheels 


32 

l 

might  be  entirely  dispensed  with.  In- 
stead of  the  rope  running  on  the  soft 
filling  of  the  wheel,  the  soft  envelope  of 
the  rope  might  run  directly  on  the  cast 
iron  rim.  Nearly  all  the  experiments  in 
this  direction  have  failed,  and  it  is  only 
very  recently  that  the  firm  of  Martin 
Stein  &  Co.,  Mulhausen,  Switzerland, 
have  solved  this  question.  They  have 
for  some  time  been  making  ropes  in 
which  coarse  cotton  yarn  was  spun  about 
the  separate  wires,  the  latter  being  then 
spun  into  rope.  In  this  way  they  ob- 
tained a  soft  body  between  the  separate 
wires,  and  also  a  soft  envelope  for  the 
whole  rope,  which,  when  saturated  with 
a  special  resinous  compound,  is  said  to 
be  very  durable.  This  kind  of  covered 
rope  stretches  much  less  than  the  com- 
mon rope.  Comparisons  made,  indicate  a 
stretch  of  only  .06  per  cent.  It  also  seems 
less  subject  to  the  variation  of  weather, 
being  partly  protected  against  sun  and 
rain  by  the  covering.  For  the  same 
reason,  rusting  is  not  likely  to  occur. 
If,  in  connection  with  these  covered 


33 

ropes,  we  also  employ  wheels  with  leath- 
er filling,  the  adhesive  force  on  the  pul- 
leys becomes  much  greater  than  in  the 
ordinary  ropes;  thus  allowing  the  trans- 
mission to  be  worked  with  much  less  ten- 
sion in  the  ropes.  If  we  desire  to  get 
the  same  cross-sectional  area  of  metal 
in  these  ropes  as  in  the  common  ones,  the 
size  of  rope  required  will,  of  course,  be 
considerably  greater,  but  the  rope  itself 
will  be  much  more  flexible.  In  this  case, 
we  can,  without  any  harm  resulting 
therefrom,  introduce  covered  wire 
centres  instead  of  using  hemp. 

Messrs.  Stein  &  Co.  have  also  been  ex- 
perimenting with  hemp  as  a  covering, 
instead  of  the  expensive  cotton  yarn, 
but  their  experiments  are  of  too  recent 
date  to  be  discussed  here. 

The  price  of  covered  wire  ropes  is,  of 
course,  greater  than  that  of  the  common 
ropes.  But  if  they  are  as  durable  as 
the  manufacturers  claim,  i.  e.,  if  they 
may  be  expected  to  last  about  ten  years, 
it  is,  of  course,  more  true  economy  to  use 
the  more  expensive  rope.  By  using 


34 

these  covered  ropes,  previously  well 
stretched,  we  may  doubtless  avoid  the 
various  difficulties  which  have  opposed 
and  prevented  the  more  general  introduc- 
tion of  the  transmission  of  power  by 
wire-ropes. 

SECTION  IV. 

THE   TENSION   ON   THE    ROPE. 

I  shall  first  present  the  demonstration 
of  the  friction  of  a  simple  band,  as  given 
in  Rankine's  "  Millwork  and  Machinery." 
A  flexible  band  may  be  used  either  to 
exert  an  effort  or  a  resistance  upon  a 
drum  or  pulley.  In  either  case,  the  tan- 
gential force,  whether  effort  or  resist- 
ance, exerted  between  the  band  and 
the  pulley,  is  their  mutual  friction, 
caused  by  and  proportional  to  the  nor- 
mal pressure  between  them. 

In  Fig.  14,  let  C  be  the  axis  of  a  pul- 
ley AB,  round  an  arc  of  which  there  is 
wrapped  a  flexible  band,  TjABT,;  let 
the  outer  arrow  represent  the  direction 
in  which  the  band  slides,  or  tends  to 
slide,  relatively  to  the  pulley,  and  the 


inner  arrow  the  direction  in  which  the 
pulley  slides,  or  tends  to  slide,  relatively 
to  the  band.  Let  Ta,  be  the  tension  of 

• 


36 

the  free  part  of  the  band  at  that  side 
towards  which  it  tends  to  draw  the  pul- 
ley, or  from  which  the  pulley  tends  to 
draw  it;  T2,  the  tension  of  the  free  part 
at  the  other  side;  T,  the  tension  of  the 
band  at  any  intermediate  point  of  its 
arc  of  contact  with  the  pulley;  6,  the 
ratio  of  the  length  of  that  arc  to  the 
radius  of  the  pulley;  dO,  the  ratio  of  an 
indefinitely  small  element  of  that  arc  to 
the  radius;  R=T1—T2=  the  total  friction 
between  the  band  and  the  pulley;  ctR, 
the  elementary  portion  of  the  friction, 
due  to  the  elementary  arc  d6;  f,  the  co- 
efficient of  friction  between  the  materi- 
als of  the  band  and  pulley.  Then  it  is 
known  that  the  normal  pressure  at  the 
elementary  arc  dB  is  TWO/  T  being  the 
mean  tension  of  the  band  at  that  elemen- 
tary arc;  consequently  the  friction  on 
that  arc  is 


Now,  that  friction  is  also  the  differ- 
ence between  the  tensions  of  the  band 
at  the  two  ends  of  the  elementary  arc; 


37 


which  equation  being  integrated  through- 
out the  entire  arc  of  contact,  gives  the 
following  formulae: 


hyp.  log.       = 


When  a  belt  connects  a  pair  of  pulleys 
at  rest,  the  tensions  of  its  two  sides  are 
equal;  and  when  the  pulleys  are  set  in 
motion,  so  that  one  of  them  drives  the 
other  by  means  of  the  band,  it  is  found 
that  the  advancing  side  of  the  belt  is 
exactly  as  much  tightened  as  the  re 
turning  side  is  slackened,  so  that  the 
mean  tension  remains  unchanged.  The 
ratio  which  it  bears  to  the  force,  R,  to 
be  transmitted,  is  given  by  this  formula: 

f6 

j 


2  (<-!) 
If  the  arc  of  contact  between  the  band 


38 


and   the  pulley,   expressed   in  fractions 
of  a  turn,  be  denoted  by  n,  then 


that  is  to  say,  e  is  the  antilogarithm, 
or  natural  number,  corresponding  to  the 
common  logarithm  2.  7288  fn. 

The  value  of  the  coefficient  of  friction, 
/",  depends  on  the  state  and  material  of 
the  rubbing  surfaces.  This  coefficient  is 
about  0.25  when  wire  rope  is  used  run- 
ning on  leather  or  gutta  percha.  In  wire 
rope  transmission  n  =  \  ;  inserting  this 
value,  and  also  the  value  of  /,  in  equa- 
tion (2),  we  get  : 

T  T  T  +T 

-  =  2.188  ;^=  1.84;   -^-'=1.84. 

In  ordinary  practice,  it  is  usual  to  as- 
sume 


2=R;  T,=2K; 


This  has  been  done  m  the  calculations  in 
this  thesis.  Therefore,  if  with  a  wire 
rope  we  wish  to  transmit  a  certain  force 


39 

P,  we  must  proportion  the  transverse 
dimensions  of  the  rope  to  bear  the  maxi- 
mum strain  that  will  come  on  it.  This 
maximum  strain  will  come  on  the  driv- 
ing side  of  the  rope  and  be  equal  to 
twice  the  force  transmitted,  i.  e.,  equal 
2  P. 

In  all  the  following  calculations,  the 
strength  of  the  hemp  core  is  left  entire- 
ly out  of  consideration,  as  it  is  only  used 
for  the  purpose  of  securing  flexibility, 
and  not  for  strength.  If  it  is  an  error 
to  leave  this  out,  it  is  only  a  slight  one, 
and  is  on  the  safe  side  at  that. 

Let  P= force  to  be  transmitted. 

a— total  cross-sectional  area  of  wires 
in  rope  in  square  inches. 

t= tension  in  pounds  per  square  inch 
of  cross-sectional  area  of  wires. 

2P 

Then  ta=2  P;  and  a= — . 
t 

n=ihe  number  of  wires  in  the  rope 

=  42. 
<?=  diameter  of  each  wire  ;  then 

7T     72  2P 

n—  d  =a=  — . 

4  t 


40 

H.P:=  number  of   horse-power   to    be 

transmitted. 

R=  radius  of  wheel  in  feet. 
N"  —number  of  revolutions  per  minute. 
Then,  by  the  proper  substitutions,   we 
get: 

(4) 

n-  Z3—  ?  X  3300°  H-  P-  —  33000  H.  P. 
n±      ~t 


*=i!?£2?!£ (5) 

After  substituting  for  n  its  value,  42,  we 

get:  

,7      ,/31.S5  H.  P.  ,flx 


To  find  the  value  of  d  from  the  pre- 
ceding equations,  we  must  know  at  the 
very  outset,  what  is  the  proper  tension 
to  use  in  the  ropes.  The  tension  in  the 
rope  is  composed  of  three  parts;  viz., 
1st,  the  tension  necessary  to  transmit  the 
required  amount  of  power  with  the 
velocity  of  the  wheel;  2d,  the  tension 
produced  by  the  bending  of  the  rope 
around  the  wheel,  causing  the  outer 


41 

fibres  of  each  wire  to  be  extended  and 
strained;  3rd,  the  tension  caused  by  the 
centrifugal  force. 

This  centrifugal  tension,  though  never 
amounting  to  much  in  ordinary  practice, 
becomes  somewhat  of  an  item  when  a 
velocity  of  nearly  a  mile  per  minute  is 
employed.  It  is  the  sum  of  these  ten- 
sions which  the  rope  is  called  upon  to 
resist. 

Determining  the  proper  tension  is,  of 
course,  equivalent  to  fixing  on  a  factor  of 
safety.  Rankine  states  that  three  and  a 
half  is  a  good  factor  for  steady  work. 
Although  this  may  at  first  sight,  seem 
rather  low,  it  must  be  borne  in  mind  that 
the  process  of  wire  drawing  is  a  process 
of  testing,  so  that  we  are  certain  of  hav- 
ing only  the  best  materials.  We  may, 
therefore,  safely  work  with  this  factor, 
but  for  the  sake  of  durability,  a  some- 
what higher  factor  seems  advisable.  In 
this  thesis,  four  (4)  has  been  taken  as 
the  factor  of  safety.  To  find  the  tension 
available  for  the  transmission  of  power, 
we  must  evidently  get  the  difference 


42 

between  the  total  tension  and  the  sum 
of  the  tensions  produced  by  bending 
and  by  centrifugal  force. 

We  will,  therefore,  pass  at  once  to  the 
consideration  of  the  tension  caused  in 
the  rope,  by  bending  the  same  around 
the  wheels. 

In  Figure  15,  let  R=  radius  of  the 

Fig.  ,5 


wheel,  d=  diameter  of  a  single  wire, 
and  E=  modulus  of  elasticity  of  wire. 
Now  it  is  apparent  that  when  the  rope  is 


43 

compelled  to  bend  to  the  curve  of  the 
wheel,  the  outer  fibres  of  each  wire  will 
be  extended  and  the  inner  ones  com- 
pressed, while  the  center  (the  neutral 
axis)  will  remain  unchanged  in  length. 
As  the  strain  varies  with  the  size  of  the 
wheel,  becoming  greater  as  the  wheel  is 
made  smaller,  and  vice  versa,  it  is  of  im 
portance  to  determine  what  should  be 
the  relation  between  the  diameters  of 
the  wire  and  of  the  wheel.  In  ordinary 
practice  this  ratio  ranges  between  1,000 
and  2,500. 

If   in   Fig.    15,  we  consider  the   arc 
which  subtends  the  angle  oC,  the  length 

of   the   neutral   axis   will  be   - —  R  OG 

1 80 

But  the  outermost  fiber  subtends  the 
same  angle  with  a  radius  R  +  -  ; 

therefore,  its  length  must  be  ^Tr 

OC.  The  amount  by  which  the  outer 
wire  has  been  extended  is  evidently  the 
difference  between  these  two  lengths  ; 
i.  e.,  the  extension 


44 


If  £o=tension  produced  in  the  rope  by 
bending,  then,  from  the  definition  of  the 
modulus  of  elasticity,  "the  quotient  ob- 
tained by  dividing  the  force  which  pro- 
duces the  displacement  by  the  amount  of 
the  extension,"  we  get 

t0— —  Roc      *0R  ™ 

E= 7 =    d   =  — y—        (8) 

TT    d  -  d 

~I802CC 

t~^d  (9) 

*°-2R 

R        E 

*-¥?     (10> 

From  these  equations  the  tension  may 
be  determined.  For  the  elasticity  of 
iron  wire  we  may  take  the  mean  of  vari- 
ous experiments;  viz.,  28,000,000  Ibs. 
Substituting  this  value  of  E  and  also 

introducing  for  d  its  value  --  ,  we  have 
9 

for  the   tension  per  square  inch  caused 
by  bending 


45 


t0  =  28060000—^=  1555555r-    .     .     (11) 
18  JLV  rC 

Substituting  in  equation  (11)  some  of 
the  probable  values  of  the  ratio  ^-,  we 

Jtx 

get  the  following  table  : 


R 
D 

to 

R 
D 

to 

40 

38888 

120 

12963 

45 

34570 

130 

11965 

50 

*31111 

140 

11111 

55 

28282 

150 

10730 

60 

25925 

160 

9722 

65 

23930 

170 

9150 

70 

22222 

180 

8642 

75 

20740 

190 

8187 

80 

19444 

200 

7777 

85 

18300 

210 

7407 

90 

17284 

220 

7161 

95 

16374 

230 

6763 

100 

15555 

240 

6481 

110 

14141 

250 

6222 

This  table  is  somewhat  interesting,  as 
it  shows  clearly  the  cause  of  the  rapid 

wear  of  the  ropes  when  running  on  small 

•p 
pulleys.     When  the  ratio  =-  is  large,  the 


46 

tension  varies  but  slightly,  with  small 
changes  in  this  ratio;  while  if  the  latter 
is  below  about  100,  the  tension  increases 

at  a  much  faster  rate  than  =r   decreases. 

T> 

On  the  one  hand,  as  the  ratio  =  decreases, 

the  wheels  become  smaller  and  less  ex- 
pensive; but,  on  the  other  hand,  we  get 
so  great  a  strain  on  the  ropes  that  they 
quickly  wear  out.  We  must,  therefore, 
seek  to  find  a  point  at  which-  the  com- 
bined resultant  economy  may  be  as  great 
as  possible.  This  will  be  considered  fur- 
ther on. 

We  will  now  take  up  the  discussion  of 
the  centrifugal  tension,  using  the  dia- 
gram in  Fig.  15. 

Let  R= radius  of  wheel  in  feet. 
w= weight  of   the  rope   per  running 
foot. 

v  =  velocity  of   the  rope   in  feet   per 
second. 

Then  the  centrifugal  forcQ=^iT-=-  .  -= 
K       g     K 


47 

But  the  tension  in  an  arc  pressed  nor- 
mally by  any  force  p  ispli;  consequent- 
ly the  centrifugal  tension 


,B'    .    .     (12) 

If  we  wish  to  express  the  velocity 
differently,  we  may  write,  when  N  = 
number  of  revolutions  per  second,  v  =  2 
n  R  N,  v2=:  4  7T2  R2  N2  ;  introducing  this 
value  of  v2,  we  have 

Z2=1.226  RaN2M   .     .     .     (13) 

While  the  rope  is  passing  around  the 
wheel,  it  is  subjected  to  a  tension  T, 
which  is  equal  to  the  sum  of  these  three 
separate  tensions.  But  in  any  given 
case,  we  may  evidently  vary  the  com- 
ponent tensions  at  pleasure,  provided  we 
keep  the  total  tension  T  constant. 

We  have  previously  (equations  (5)  and 
(6)  )  determined  the  diameter  of  the 
wires  in  terms  of  the  tension  t.  But 
we  now  wish  to  introduce  the  total  ten- 
sion T,  into  this  formula.  Bearing  in 
mind  that  t  —  T  —  t0  —  t#  and  multiply- 


48 

ng  equation  (5)  by  the  value  of  d,   in 
equation  (10),  we  get 

132000         2t0  HP 

-"*X~~ 


.P.       t_0 
I 


Having  now  obtained  an  equation  in- 

troducing the  ratio  -,    we    must    know 
* 

how  this  is  to  be  determined,  i.e.,  what 
conditions  control  the  magnitude  of  t0 
and  t  with  respect  to  T. 

(In  all  the  following  calculations,  the 
centrifugal  tension  £2.-  is  not  taken  into 
consideration,  as  it  only  amounts  to  250 
pounds,  even  in  an  extreme  case.  This 
is  a  small  quantity  compared  with  the 
other  tensions  on  the  rope,  and  would 
lead  to  a  needless  complication  of  for- 
mulae). These  conditions  are  two  in 
number;  1st,  the  size  of  wheel  that  may 
conveniently  be  employed;  2nd,  the  re- 
sulting deflection  or  sag  in  the  ropes,  the 
latter  being  again  subject  to  various  con- 
ditions, such  as  the  available  height,  etc. 


49 

We  will  now  pass  to  the  consideration 
of  the  1st  condition;  viz.:  the  size  of 
the  wheels.  As  previously  remarked, 
the  value  of  R  varies  immensely  with 
changes  of  t  and  t0.  The  diameter  of 
the  wheel,  however,  is  always  very  large, 
so  that  it  becomes  interesting  to  know 
under  what  conditions  it  assumes  its 
smallest  value.  The  first  step  is  to  obtain 
a  perfectly  general  formula  for  R.  This 
is  done  by  multiplying  equation  (14)  by 
the  cube  of  equation  (10)  which  gives 
as  its  result 

264000RP.          *0E 

;r'rcN      X-CT-O 
Differentiating  this  equation,  we  get 


To  find  the  conditions  under  which  R 
will  assume  its  minimum  value,  we  must 
place  the  first  differential  coefficient 
equal  to  zero.  Doing  this,  we  get,  after 
transposing  and  reducing 

3£02  /.  £0=JT.     .     .     .     (16) 
t=%t0      .     .     .     .  (17) 


50 

This  relation,  being  independent  of 
the  number  of  wires  and  of  the  shape  of 
the  rope,  will  of  course  hold  good  for 
a  rope  of  any  size  and  of  any  shape  of 
cross-section.  This  shows  the  adapta- 
bility of  this  last  formula  to  ropes  of 
flat  or  rectangular  cross-section,  which 
have  been  used  to  a  limited  extent  for 
transmitting  power.  From  this  formula, 
we  see  that  in  the  case  most  favorable  to 
small  size  of  wheels,  the  tension  caused 
by  bending  is  twice  as  great  as  the  direct 
tensional  strain.  The  minimum  value  of 
R  is,  however,  rarely  used  in  practice, 
for  a  reason  which  will  be  shown  pres- 
ently. It  may,  however,  be  remarked 
here,  that  with  a  small  working  tension 
£,  the  deflection  or  sag  of  the  rope  is 
greater  than  that  with  an  increased  ten- 
sion; so  that  in  determining  the  ratio  -° 

t 

we  must  take  into  consideration  the 
available  height  of  the  wheels  above  the 
ground.  This  point  will  be  considered 
in  the  next  section. 


51 


SECTION  V. 

THE    CATENARY. 

If  a  rope  or  other  flexible  continuous 
line  be  secured  at  two  points  and  loaded 
continuously  between  them  according  to 
any  law,  it  will  assume  some  definite 
curvilinear  form.  When  the  load  is  the 
weight  of  the  rope  only,  the  curve  is 
called  a  "  catenary." 

Suppose  that  the  rope  is  fixed  at  the 
points  A  and  B  (see  Fig.  16),  and  that 
the  only  force  in  operation  is  the  weight 
of  the  rope,  i.  e.  the  load  is  a  continuous 
and  direct  function  of  the  length  of  arc. 
Take  the  origin  of  co-ordinates  at  any 
point  on  the  curve  (C0),  the  axis  of  Y 
being  vertical  and  the  axis  of  X  horizon- 
tal. All  our  forces  being  in  one  plane, 
the  axis  of  Z  is  of  course  unnecessary. 
Let  t  '—  tension  at  any  point,  as  a. 

to=  tension  at  the  origin  C0. 
X0=  horizontal  component  of  the  ten- 

dx' 

sion  at  U0=£0  -=- 
cf/s 

Y0=  vertical  component  of   the  ten- 
sion at  Cn=tn  -%- 


52 

X  =horizontal  component  of  applied 
forces  between  C0  and  a. 

Y=vertical  component  of  applied 
forces  between  C0  and  a. 

-7-,  TT,   will  be   the   cosines   of    the 
ds'  ds* 

angles  which  the  curve  makes 
with  its  respective  axes,  and  re- 
solving t'  we  have 

dx 
t'  —  =  horizontal  component  of  tension, 

t'-j-=  vertical  component  of  tension, 

Consequently,  from  the  principles  of 
Mechanics,  we  must  have,  for  equilibrium 


T+Y.-M=0 

These  equations  are  perfectly  general 
for  any  case  in  which  the  applied  forces 
are  in  one  plane. 

To  get  a  more  definite  result  for  the 
case  under  consideration,  we  will  take 
the  origin  at  the  lowest  point  C,  and  the 


54 

axis  of  X  tangent  to  the  curve  at  that 

point:  this  will  make  -7-  =  !  and  -fr-=rO: 

ds  ds 

as   the   weight   acts   vertically,   X  =  0. 
With  these  substitutions  we  get 
dx 


ds 

Let  w=  weight  per  running  foot  of  rope, 
and  s—  length  of  curve  in  feet;  then  ws= 
weight  of  the  rope;  and  as  this  is  the 
only  vertical  force,  we  have  ws=Y. 

This  reduces  the  above  equations  to 
the  following  : 

dx 

T  \  •••  <« 

,dy 

t'-?-  =  ws 
ds          j 

Equation  (20)  shows  that  the  horizon- 
tal component  of  the  tension  is  equal  to 
the  tension  at  the  lowest  point,  i.  e.,  the 
horizontal  component  of  the  tension  is 
constant  throughout  the  curve.  We  also 
observe  that  the  vertical  component  of 
the  tension  at  any  point  is  equal  to  the 


55 

weight  of  so  much  of  the  rope  as  comes 
between  the  origin  and  the  point  consid- 
ered. 

Dividing  the  first  of  equations  (20)  by 
the  second,  we  get 

—  =?£-  (21) 

dy      ws 

which  shows  that  the  tangent  of  the 
angle  varies  inversely  as  the  weight  of 
the  rope. 

Differentiating  equation  (21)  we  have 

~d89  but  da  =  (dx*  +  dy*}*  = 

V 


I        di/*\ 
(1  +  ~] 


~]  dx.     Substituting  this  value, 
we  have,  after  transposing 


*" 


Integrating  equation  (22),  we  obtain 


This  may  be  written  e  *» 


56 

transposing,  we  get 
IPX 

dx      \         clx 

Squaring  this  equation  we  get 
2wx      wx 


_2+-=l+          ,          (23) 
dx       dx*  dx* 

Reducing  and  clearing  of  fractions,  we 
get 

ICX  —WX 

-  (24> 


Integrating  the  above  equation,  we  ob- 
tain 

wx      -wx 


—wx 

(25) 


which  is  the  equation  of  the  catenary. 
To  bring  this  equation  into  a  simpler 
and  more  manageable  form,  we  will 
transfer  the  origin  of  coordinates  to  Ci, 


57 

making  CCi  =  A      Then  our  new  ordi- 
w 

nates  will  be  equal  to  y+-,   so    that    the 
last  equation  may  be  written 

WX          —  IOX  . 

(26) 

But  in  making  this  change  of  origin, 
-~y  the  tangent  of  the  angle  a  evidently 
remains  constant,  and  having  previously 

found  -f — — ,  we  will  substitute    this 
dx      t0 

value  in  equation  (24),  giving  rise  to  the 
following  value  for  the  length  of  arc: 

wx      —wx  , 

0  — e 

Squaring  equations  (26)  and  (27),  we  get 
2  wx  —  2wx  . 

.    (26a) 


58 
2  wx  —  2  wx  , 


Subtracting  (27<z)  from  (26a),  we  have 


*=*.•-     •   •   •   (28) 

Equation   (28)   gives  us  the  length  of 
arc  when  the  running  weight  of  the  rope, 

and  the  ratio  — ,  are  known.     The  weight 
w 

of  the  rope  is  always  known  in  any  given 


To  find  the  val  je  of  -°,  we  proceed  as 
w* 

follows  : 

Let  A  =  total  deflection  or  greatest  ordi- 

nate  of  the  curve. 
S=span  between  supports. 
Then,  for  the   lowest  point,  the  ordi- 

nate  is  y  =  A  +  — ;  and  the  abscissa  aj= 
w 

\  S.     Substituting  these  values  in  equa- 
tion (26)  and  reducing,  we  get 


59 

2  A 


(29) 


The  equation  just  found  is  not  sus- 
ceptible of  a  direct  solution;  so  that  it 
becomes  necessary  to  find  the  value  of 

—  by  a  method  of  approximation.     This 

will  be  done  in  the  next  section  (VI). 

Let  L=total  length  of  rope  between 
supports;  then  from  equation  (28), 

_  (30) 


To  find  the  tension  at  any  point,  we 
know  that  from  the  parallelogram  of 
forces 


We  substitute  in  this  equation  the 
values  obtained  from  equation  (20),  and 
get 


(31) 


60 

The  tension  t'  is  a  maximum  at  the  high- 
est  points.      The    ordinates    for    these 

t 
points  being  A  +  — ,  we  have 


\         wl  ° 

The  vertical  component  of  the  tension  at 
the'  highest  point  is,  of  course, 


ws=w\/y*_t_L  = 

The  tangent  of  the  angle  a,  which  the 
curve,  at  the  highest  point,  inakes  with 

*  «r    .  ws        ML 

the  axis  of  X,  is  tan  a  =  —  =  —  = 


We  have  now  developed  all  the  necessary 
equations  of  the  catenary  ;  but  before 
applying  them,  a  few  remarks  on  the 
peculiarities  of  the  curve,  as  shown  by 
its  equations,  may  not  be  out  of  place. 

Equation  (26)  shows  that  the  catenary 
rises  symmetrically  on  both  sides  of  the 


61 

axis  of  Y,  and  becomes  parallel  to  the 
same  only  at  an  infinite  distance. 

The  angle  «  increases  with  the  ordinate 
y ;  when  y  becomes  infinite,  «  =  90°  ; 
when  y  =  o,  a  =  o. 

The  line  CO,,  (- -)  is  called  the  para- 
meter of  the  curve  ;  and  the  line  BBt, 
last  used  as  the  axis  of  abscissas,  is 
called  the  directrix. 

The   value   of   the   ratio  —  varies  be- 
10 

tween  zero  and  infinity.  —   =  o  when  A 

J    w 

=  oo  ;  for  in  this  case  the  two  exponents 
in  equation  (26)  also  become  zero  ;   — = 

oo ,  when  A  =  0,  because  the  two  expo- 
nents then  each  equal  unity.     The  value 

of  —  is  always   very  large,  when    A    is 

small,   as   it   always   is   in  transmitting 
power  .by  wire  rope. 

As  will  be  seen  from  equations  (31) 
and  (32),  the  tension  in  the  rope  is  di- 
rectly proportional  to  the  weight  of  the 


62 

latter.  The  tension  reaches  its  maximum 
at  A  and  B,  and  has  its  minimum  at  C, 
where  t'  =  t0. 

When  A  is  small,  there  is  very  little 

difference  between  tn  and  t'  :  and  as      is 

10 

always  very  large,  the  results  obtained 
from  equations  (29)  and  (31)  will  not 
differ  greatly. 

The  tension  t'=t0=<x>,  when  A  =  o/ 
this  shows  the  impossibility  of  stretching 
a  rope  so  as  to  be  perfectly  horizontal  ; 
because  even  when  it  is  hauled  as  taut  as 
may  be,  there  must  always  be  a  finite 
value  of  A  existing. 

SECTION  VI. 

APPROXIMATE  SOLUTION  OF  CATENARY. 

In  practically  applying  the  preceding 
equations  of  the  catenary,  we  meet  with 
considerable  difficulty,  which  is  owing  to 

the  fact  that  the  parameter  —  can  only 

be  obtained  from  a  transcendental  equa- 
tion. 


63 

But  in  such  work  as  forms  the  subject 
of  this  thesis,  we  can  pursue  a  frequently 
used  method  of  approximation,  which  is 
abundantly  accurate  for  all  our  purposes. 
The  exact  equations  of  the  catenary,  as 
we  have  deduced  them,  are  of  course 
applicable;  but,  as  we  have  left  the  stiff* 
ness  of  the  rope  out  of  consideration,  and 
assumed  it  to  be  "  perfectly  flexible,"  the 
shape  of  the  curve  is  not  expressed  with 
mathematical  exactitude  by  even  these 
equations.  For  this  reason  alone,  it 
might  be  permissible  to  use  approximate 
formulae ;  but  we  have  a  still  greater 
right  to  use  them,  because  the  deflec- 
tion A  is  always  a  very  small  fraction  of 
the  span  S,  and,  therefore,  the  parame- 
ter —  is  always  very  large. 

Consequently,  in  equation  (29),  the 
exponent  —  is  a  small  fraction  ;  and 

0 

we   can,  without  committing  any  great 
error,  express  its  value  by  the  series 

w  S 


64 


2  X  3  X  8 

Taking  the  first  four  terms  of  these 
series,  and  substituting  them  in  equa- 
tion (29),  we  get 

t,_          2A  2A  S9 

w~        w^  "W'S'-SA        •    (35> 

f4C~  4«0« 

Substituting  the  same  terms  of  a  simi- 
lar series  in  equation  (26),  we  get 


tn     wx* 

™=^. 

S'      wx 


0 

This   is   the   equation   of  a  parabola 

S2 
having  a  parameter  of  —  ;  so  that  our 

method  of  approximation  has  led  us  to 
consider  the  curve  as  a  parabola. 

j.  02 

Substituting  the  value  —  =-—  in  equa- 


65 


tion  (30),  we  get  for  the  length  of  the 
curve  between  supports 


By  reference  to  the  figure,  it  will  be 
seen  that  this  is  equivalent  to  assuming 
that  the  length  of  the  curve  is  equal  to 
'  twice  the  length  of  the  chord  of  half 
the  curve.  All  the  formulae  previously 
found  now  become,  by  the  proper  sub- 
stitutions 


(38) 


w  Ss 


,.  =  _      ........    (39) 


.      .      .      (40) 


By  means  of  these  formulae,  it  becomes 
an  easy  matter  to  investigate  the  various 
problems  which  present  themselves. 


66 
SECTION  VII. 

DEFLECTION    OF   THE    ROPE. 

In  order  that  the  rope  may  be  sub- 
jected to  a  proper  tension,  the  deflection 
or  sag  must  be  of  a  certain  magnitude 
while  the  rope  is  at  rest ;  we  must  also 
know  the  sag  of  the  rope  while  in 
motion,  in  order  to  estimate  the  neces- 
sary elevation  of  the  wheels.  There  are 
therefore  three  deflections  which  we 
must  determine  :  1st,  that  of  the  driving 
side  while  in  motion  ;  2nd,  that  of  the 
following  side  while  in  motion;  3rd,  that 
of  both  sides  when  the  rope  is  at  rest. 
Let  the  deflection  at  rest  be  called  A  0. 
"When  we  start  one  of  wheels,  the  driv- 
ing side  of  the  rope  rises  and  the  fol- 
lowing side  is  depressed,  until  the  dif- 
ference of  their  tensions  is  equal  to  the 
force  to  be  transmitted,  when  the  driven 
wheel  will  begin  to  move ;  in  this  con- 
dition we  will  call  the  deflection  of  the 
driving  side  A  l  and  that  of  the  follow- 
ing side  A .,. 

We  must  know  the  deflection  at  rest, 


67 

A0,  in  order  to  determine  the  proper 
length  of  rope  ;  so  that  when  it  is  put 
on  and  spliced,  we  may  feel  certain,  that 
there  will  be  neither  any  slipping  during 
the  motion,  nor  any  serious  strain  on  the 
rope  itself.  The  deflections  A  t  and  A  2, 
as  before  stated,  must  be  known,  in 
order  to  determine  in  advance,  what 
position  the  ropes  will  take  while  in 
motion,  how  near  they  will  approach  the 
ground  or  other  obstructions,  and  how 
many,  if  any,  carrying  sheaves  are  re- 
quired. 

By  solving  equation  (38)  for  A,  we 
get  for  the  value  of  the  deflection 

(42) 

8 

Now,  we  have  seen  in  Section  IV,  that 
if  the  force  at  the  circumference  of  tl^e 
wheel  is  P,  then  to  find  the  deflection  A  i 
of  the  driving  side,  t'=2  P.  To  find 
the  deflection  A2  of  the  following  side, 
t'  —  P.  Lastly,  to  find  the  deflections  A9 
of  both  sides  while  at  rest  t'—  JP. 

In  applying  equation  (42)  and  all  other 


equations  containing  t'9  it  is  to  be  borne 
in  mind  that  t'  is  not  the  tension  per 
square  inch,  but  is  the  whole  tension  on 
the  rope. 

From  this  equation,  it  is  evident  that 
the  tension  has  a  great  influence  on  the 
deflection  of  the  rope.  This  is  best 
shown  by  an  example.  Suppose  that, 
with  a  span  of  400  feet,  we  are  using 
a  ii  inch  rope  working  under  a  tension 
of  3,000  pounds.  By  making  the  proper 
substitutions  in  equation  (42)  we  get 
^  _  3000  _  //  3000  \a_(400)8_2  g  ft 

1-3*2      "\i:372/     "T~ 
Now  if  we  had  the  same  rope  working 
under  a  tension  of  only  2,400  pounds,  the 
deflection  would  be 


A  = 


___< 
1.372      V  Vl.872/  8 

Tims,  a  difference  in  tension  of  only  600 
pounds,  causes  a  difference  in  deflection 
of  three  feet. 

In  both  these  cases,  the  rope  will  work 
equally  well,  if  the  size  of  the  wheel  has 
been  properly  selected  ;  but  in  most 


cases,  it  is  not  a  matter  of  indifference 
whether  the  rope  has  a  deflection  of  two 
feet  or  of  five  feet. 

The  smaller  deflection  is  usually  to  be 
preferred,  as  it  requires  a  less  elevation 
for  the  wheels.  On  the  other  hand,  with 
a  very  short  span  the  greater  deflection 
is  generally  preferable. 

It  is,  therefore,  evident  that  we  cannot 
1  decide  on  any  definite  tension  to  be  used 
in  all  cases,  but  that  we  must  select  it 
for  every  different  case,  using  a  greater 
tension  as  we  want  a  less  deflection,  and 
vice  versa. 

But  in  order  that  the  rope  may  work 
equally  well  in  any  case,  we  must,  as 
previously  explained,  keep  the  sum  of 
the  various  tensions  constant,  i.  e.,  equal 
to  the  ultimate  strength  of  the  rope  di- 
vided by  the  factor  of  safety.  By  a 
proper  adjustment  of  the  tension,  we 
can,  in  nearly  all  cases,  bring  the  deflec- 
tion to  any  desired  amount ;  but  there 
is  still  another  way  to  accomplish  this 
end,  as  follows  : 

Generally,  we  are  not  compelled    to 


make  the  upper  side  of  the  driving  rope 
act  as  the  driving  side,  but  we  can  often 
use  the  lower  side  for  this  purpose.  In 
that  case  the  greater  deflection  of  the 
lower  side  takes  place  while  the  rope  is 
at  rest  (See  Fig.  17).  When  in  motion, 
the  lower  side  rises  above  this  position, 
and  the  upper  side  sinks,  thus  enabling  us 
to  avoid  obstructions,  which,  by  the  other 
way  would  have  to  be  removed'  Of 
course  this  expedient  cannot  always  be 
employed,  as  the  upper  side  of  the  rope 
must  not  be  allowed  to  sink  so  far  as  to 
pass  below  or  even  to  touch  the  lower 
side.  If  this  occurs,  the  rope  begins  to 
sway  and  jerk  in  a  serious  manner,  wear- 
ing out  very  rapidly. 

The  shortest  distance  between  the 
ropes  is  2  R  — (A2 — A  t).  We  must, 
therefore,  always  be  careful,  in  using 
this  plan,  to  see  that  2  R>AQ  —  A  x. 
This  result  may  often  be  obtained  by  a 
judicious  selection  of  the  tension,  and  of 
the  diameter  of  wheel. 

By  the  application  of  the  equations 
given  in  this  and  the  preceding  sections, 


71 


72 


we  may  solve  all  the  problems  which 
present  themselves  in  designing  a  wire- 
rope  transmission.  The  following  table 
which  is  taken  from  Mr.  W.  A.  Roebling's 
pamphlet,  previously  referred  to,  will  be 
found  of  great  value  in  designing,  giving 
as  it  does,  the  most  suitable  proportion 
for  general  use.  Its  use  is  self-evident  ; 
and  it  need  only  be  remarked,  that  where 
there  is  a  choice  between  a  small  wheel 
with  fast  speed,  and  a  larger  wheel  with 
slower  speed,  it  is  usually  preferable  to 
take  the  larger  wheel. 

TABLE  OF  TRANSMISSION  OF  POWER  BY 
WIRE-ROPES. 


Diame- 
ter of 
Wheel 
in  Feet. 

Number 
of 
Revolu- 
tions. 

Trade 
No.  of 
Rope. 

Diame- 
ter of 
Rope. 

Horse 
Power. 

4 
4 
4 
4 
5 
5 
5 
5 
6 

80 
100 
120 
140 
80 
100 
120 
140 
80 

23 
23 
23 
23 
22 
22 
22 
22 
21 

1 
I 

S 

3.3 
4.1 
5. 
5.8 
6.9 
8.6 
10.3 
12.1 
10.7 

73 


Diame- 

Number 

Trade 

Diame- 

ter of 
Wheel 

of 
Revolu- 

No. of 

ter  of 

Horse 

in  Feet. 

tions. 

Rope. 

Rope. 

Power. 

6 

100 

21 

H 

13.4 

6 

120 

21 

la 

16.1 

6 

140 

21 

3$ 

18.7 

7 

80 

20 

i 

16.9 

7 

100 

20 

i 

21.1 

7 

120 

20 

* 

25.3 

7 

140 

20 

i 

29.6 

8 

80 

19 

22. 

8 

100 

19 

1 

27.5 

8 

120 

19 

| 

33. 

8 

140 

19 

| 

38.5 

QA 

20 

40. 

9 

OU 

19 

i      1 

41.5 

9 

100 

20 
19 

50. 
51.9 

9 

120 

20 
19 

i    1 

60. 
62.2 

9 

140 

20 
19 

i    i 

70. 
72.6 

10 

80 

19 

18 

114 

55. 
58.4 

10 

100 

19 

18 

l-.tt 

68.7 
73. 

10 

120 

19 

18 

fl4 

82.5 
87.6 

10 

140 

19 

18 

96.2 
102.2 

11 

80 

19 

in 

64.9 

18 

75.5 

11 

100 

19 

IH 

81.1 

18 

94.4 

74 


Diame- 
ter of 
Wheel 
in  Feet. 

Number 
of 
Revolu- 
tions. 

Trade 
No.  of 
Rope. 

Diame- 
ter of 
Rope. 

Horse 
Power. 

11 

120 

19 

f  H 

97.3 

18 

113.3 

11 

140 

19 

Mi 

113.6 

18 

132.1 

12 

80 

18 

n  i 

93.4 

17 

99.3 

12 

100 

18 

HI 

116.7 

17 

124.1 

12 

120 

18 

fti 

140.1 

17 

148.9 

12 

140 

18 

li  t 

163.5 

17 

173.7 

13 

80 

18 

iiri 

112. 

17 

122.6 

13 

100 

18 

HI 

140. 

17 

153.1 

13 

120 

18 

H  I 

168. 

17 

183.9 

14 

80 

17 

i    i 

148. 

16 

141. 

14 

100 

17 

f  1 

185. 

16 

176. 

14 

120 

17 

I  * 

222. 

16 

211. 

15 

80 

17 

f  i 

217. 

16 

217. 

15 

100 

17 

t  1 

259. 

16 

259. 

15 

120 

17 

f  * 

300. 

16 

300. 

SECTION  VIII. 

LIMITS     OF     SPAN. 

It  becomes  interesting  to  know  be- 
tween what  limits  the  span  may  vary, 
without  giving  impracticable  results. 

The  least  practicable  span  is  that  in 
which  the  deflection  of  the  rope  becomes 
so  small,  that  the  latter  cannot  be  hung 
freely  on  the  driving  wheels,  so  that 
special  tightening  devices  must  be  used. 
»  As  such  may  be  mentioned  tightening 
sheaves  and  moveable  pillow-blocks.  Of 
course  it  cannot  be  claimed  that  such  de- 
vices make  the  transmission  too  compli- 
cated, but  this  merely  changes  the  inves- 
tigation for  the  lower  limit  of  the  span 
into  one  for  the  limit  at  which  such 
special  devices  become  necessary.  To 
find  the  minimum  value  of  the  span  we 
proceed  as  follows  :  From  equation  (38) 
we  get  an  expression  for  the  span  in 
terms  of  tf,  w  arid  A . 


By   placing   the   minimum   allowable 


values  of  A  and  —  in  this  equation,  we 

will  get  an  expression  for  the  smallest 
value  of  S.  We  will  therefore  assume 
that  the  deflection  shall  never  be  less 

than  8  inches  —  §  foot,  and  that  the  ratio 

£/ 

—  shall  never  go  below  500.    Introducing 


these  values  we  get  S  =  A/~8^<~|7^00—  ?) 
=  51.6  feet.     We  thus  see  that  the  limit 


77 


is  very  low,  allowing  us  to  use  a  free 
transmission  for  so  short  a  distance  as 
5 1  feet.  Below  ffliis,  shafting  will  usually 
be  found  preferable  and  less  trouble- 
some. 

Fig.,  9 


78 

When  the  distance  of  transmission 
materially  exceeds  three  or  four  hundred 
feet,  or  when  there  is  not  sufficient  height 
available  for  the  sag  of  the  rope,  the 
latter  must  be  supported  at  intermediate 
points  by  carrying  sheaves.  Sometimes 
it  is  sufficient  to  support  only  the  lower 
following  side  of  the  rope,  and  gene- 
rally, whatever  the  number  of  sheaves, 
the  driving  side  is  supported  at  one  less 
point  than  the  following  side.  The  same 
number  of  sheaves  may,  however,  be 
used,  placing  one  over  the  other.  The 
sheaves  must  never  be  placed  side  by 
side,  as  has  been  sometimes  done  to  the 
great  detriment  of  the  transmission.  To 
save  still  more  room,  we  may,  where 
practicable,  make  the  lower  rope  the 
driving  side,  as  previously  explained. 

The  manner  of  arranging  carrying 
sheaves  and  intermediate  stations  is 
shown  in  Figures  18-29  inclusive.  The 
sheaves  supporting  the  driving  side  of 
the  rope  must  in  all  cases  be  of  equal 
diameter  with  the  driving  wheels  ;  and 
this  for  the  same  reason  that  the  latter 


79 

are  usually  made  of  so  large  a  diameter. 
For  whether  the  rope  laps  half  way  round 
on  the  driving  wheels,  or  only  quarter 
way  round  on  the  carrying  sheaves, 
makes  no  difference  ;  the  tension  due  to 
bending  is  the  same  in  both  cases.  With 
the  following  side,  however,  a  somewhat 
smaller  wheel  may  be  used,  owing  to  the 
fact  that  there  is  less  strain  on  this  side, 
and  it  is  therefore  better  able  to  stand 
4he  additional  tension  due  to  bending. 

The  system  of  carrying  sheaves  may 
generally  be  replaced  by  that  of  inter- 
mediate stations.  When  this  is  used,  we 
have  at  each  station,  instead  of  two  car- 
rying sheaves,  one  double  grooved  wheel. 
The  rope,  instead  of  running  the  whole 
length  of  the  transmission,  runs  only 
from  one  station  to  the  other.  It  is  ad- 
visable to  make  the  stations  equidistant, 
so  that  a  rope  may  be  kept  on  hand, 
ready  spliced,  to  put  on  the  wheels  of 
any  span,  should  its  rope  give  out.  This 
method  is  greatly  to  be  preferred  where 
there  is  sometimes  a  jerking  motion  to 
the  rope,  as  it  prevents  the  rope  from 


transmitting  any  sudden  movements  of 
this  kind. 

The   supports   for    the    stations    are 
various.     They  range  in  dimensions  and 


83 

style  from  the  simple  wooden  frame 
shown  in  Fig.  18,  and  the  iron  one  of 
Fig.  19,  to  the  more  ornamental  form  of 
masonry  (Figs.  20  and  21),  and  then  to 
such  immense  masses  of  masonry  as  are 
shown  in  Figures  22-29.  In  Europe,  the 
supports  are  usually  built  of  masonry, 
while  in  this  country,  wood  is  chiefly  used, 
beingbolted  to  a  masonry  foundation  be- 
low the  reach  of  frost.  (In  connection 
with  Figures  20  and  21,  I  may  say  that 
the  wheel  there  shown  is  one  that  is  just 


84 

coming  into  use.  It  consists  of  a  cast 
iron  hub  and  a  rim,  which  are  united  by 
sixteen  tension  rods.)  When  a  wooden 
frame  is  made  to  support  the  wheel,  it 

Fig.  24, 


85 


must  be  firmly  braced  side-ways,  to  keep 
the  wheel  in  the  proper  plane,  but  end- 
bracing  is  not  required,  as  there  is  no 
tendency  to  push  it  in  either  direction. 

To  find  the  pressure  on  the  bearings  of 
one  of  the  double-grooved  wheels,  the 
simplest  method  is  by  construction. 
Make  A  B=  and  ||  T,  B  C,=  and  ||  T0 
C  D=  and  ||  t,  D  E=  and  ||  tl9  E  F  ver- 


Compagnie  Generate  de  Bellegarde. 
Carrying  Sheaves  (3,150  Horse-Power). 


86 

tical  and  =  the  weight  of  the  pulley  and 
shaft,  then  the  line  connecting  A  and  E 
is  the  intensity  and  direction  of  the  re- 
sulting pressure.  (See  Figures  30  and  31.) 
When  the  rope  is  put  on  the  wheels,  it  is 
best  to  use  an  arrangement  similar  to 
that  shown  in  Figures  32  and  33.  It  is 
bolted  to  the  rim  of  the  wheel  as  shown. 
If  it  is  required  to  change  the  direc- 
tion of  the  rope  at  some  station,  it  can 
be  done  by  the  interpolation  of  horizon- 
tal sheaves,  or  by  connecting  the  vertical 
driving  wheels  by  bevel-gear.  The  lat- 
ter is  more  usually  employed.  (See 
Figures  34  and  35.) 

SECTION  IX. 

SPECIAL   CASES. 

It  sometimes  happens,  that  the  two 
wheels  are  not  at  the  same  height,  as 
has  been  hitherto  supposed,  but  that  one 
is  at  a  higher  level  than  the  other.  This 
frequently  happens  where  it  is  desired  to 
use  the  power  of  waterfalls  in  a  ravine, 
or  in  conducting  power  up  or  down  the 


side  of  a  hill.  The  rope  then  takes  a 
position  similar  to  that  shown  in  Fig.  36. 
If  the  difference  in  height  is  slight, 
we  can  make  use  of  the  formulae  already 
found,  without  any  serious  error.  But 
if  it  is  great,  we  must  take  a  different 
way.  for  in  this  case  the  tensions  at  the 
points  of  support  are  not  the  same,  the 
lower  one  having  a  less  tension  than  the 
one  above.  This  somewhat  complicates 
the  problem,  causing  us  to  proceed  as 
follows  :  We  first  make  all  the  calcula- 
tions for  the  lower  wheel  with  the  deflec- 
tion A  {  and  the  span  2S, ;  we  then  find 
the  tension  in  the  rope  at  the  upper 
wheel,  and  proportion  the  diameter  of 
the  latter  according  to  rules  previously 
given,  so  that  the  total  tension  shall  not 
exceed  the  ultimate  strength  divided  by 
the  factor  of  safety.  To  do  this  we 
must  first  determine  St  ;  this  can  easily 
be  done  from  the  property  of  the  para- . 
bola  that 


^  =  8—. ^^ ; 

V  A  ,  +  V  A  , 

I-  ' 


Fig.26 


89 

when  S  =  horizontal  distance  between 
the  points  of  support. 

The  quickest  and  most  usually  em- 
ployed method  of  getting  the  value  of 
S,  is  the  following.  An  accurate  scale- 
drawing  is  made  of  the  plan  in  which 
the  rope  is  to  be  placed. 

This  drawing  is  set  vertically,  and  a 
fine  phain  is  fastened  or  held  with  its 
two  ends  at  the  points  of  support,  until 

Fig.  27. 


Fig.  28. 


91 

a  proper  deflection  is  obtained.  It  then 
becomes  a  matter^  of  ease  to  measure  S, 
and  S2,and  to  make  all  the  necessary  calcu- 
lations. We  can,  in  this  way,  try  different 
deflections  and  observe  their  suitability 
to  the  design,  but  must  always  bear  in 
mind,  whether  we  are  getting  the  deflec- 


Intermediate  Station  (3,150  Horse- 
Power). 

Compagnie  General  e  de  Bellegarde. 
(See  Engineer,  vol.  37,  1874.) 


92 

tion  of  the  driving  or  of  the  following 
side  or  that  of  both  sides  at  rest.  This 
method,  though  not  giving  as  great  ac- 
curacy as  the  solution  of  the  above  equa- 
tion, is  nevertheless  largely  used  in  prac- 
tice, owing  to  its  great  convenience.  It 
may  be  used  when  the  pulleys  are  on 
the  same  level,  showing  between  what 
limits  we  can  work. 

Another  peculiar  case  is  when  the  rope 
rises  nearly  in  a  vertical  direction.  This 
is  the  limiting  case  of  the  inclined  trans- 
mission. The  rope  produces  no  tension 
whatever  on  the  lower  wheel,  while  at 
the  upper  wheel  the  tension  is  only 
equal  to  the  weight  of  the  rope.  Even 
this  last  tension  is  such  a  small  quantity 
as  to  be  left  entirely  out  of  considera- 
tion, and  we  are  consequently  obliged  to 
use  some  device  for  producing  the  re- 
quisite tension.  Figures  37,  38  and  39 
show  various  ways  of  accomplishing  this 
object  by  means  of  tightening  sheaves. 
In  Fig.  38,  as  the  rope  passes  around 
the  wheel  twice,  the  same  must  be  pro- 
vided with  two  grooves.  Instead  of 


93 

these  tightening  sheaves,  we  may,  when 
practicable,  put  up  two  carrying  sheaves 
as  shown  in  Fig.  39,  so  as  to  have  hori- 
zontal stretch  enough  to  obtain  the  ten- 
sion necessary. 

SECTION  X. 

>  PRACTICAL   DIFFICULTIES. 

In  the  transmission  of  power  by  wire 
ropes,  the  greatest  attention  must  be 
paid  to  keeping  the  ropes  and  the  lining 
of  the  wheels  in  thorough  repair.  Even 
when  the  ropes  are  exceedingly  taut  on 
the  wheel  at  first,  it  has  been  found  by 
experience  that,  after  a  short  time,  the 
ropes  stretch  considerably.  This  causes 
the  ropes,  particularly  in  summer,  to  sag 
so  much  as  to  incapacitate  them  from 
transmitting  the  whole  force,  causing 
them  to  slip  on  the  wheels;  or  the  ropes 
begin  to  drag  on  the  ground  or  other 
obstructions.  This  evil  may  be  partially 
remedied  by  shortening  and  again  spli- 
cing the  rope,  which,  however,  should  be 
avoided  as  long  as  possible,  as  the  rope 


94 


is  ruined  more  rapidly  by  several  re- 
splicings,  than  by  long  running  under 
the  regular  working  tension.  I  must 
remark  that  a  wire  rope  stretches  more 
as  the  wires  make  a  greater  angle  with 
the  axis  of  the  rope;  but  as  a  rope  hav- 
ing its  wires  parallel  to  the  axis  would 


95 


be  useless,  we  must  strive  to  keep   the 
angle  at  its  minimum  value. 

Experiments  made  with  a  view  to 
stretching  the  ropes  before  putting  them 
into  use  have  not  been  very  successful. 


96 

It  is  only  lately  that  the  problem  has 
been  partially  solved  by  a  method  of 
compressing  the  ropes  while  subjecting 
them,  at  the  same  time,  to  a  great  ten- 
sional  strain.  Wire  ropes  with  wire 


centers,  as  sold  in  the  market,  are  stretch- 
ed in  this  manner  from. 22  to  1.2  percent. 
Wire  ropes  with  hemp  centers,  as  gen- 
erally employed  for  the  transmission  of 
power,  are  stretched  from  .71  to  2.6 


97 

per  cent,  of  their  original  length,  with- 
out at  all  impairing  their  strength. 

Although  this  is  a  great  step  in  ad- 
vance, reducing  the   stretching   of  the 

F'g-33 


rope,  with  its  accompanying  disturb- 
ances, to  a  minimum,  yet  even  this  is 
not  sufficient  to  maintain  a  constant  ten- 


98 

sion  and  deflection  in  the  rope,  and  we 
are  often  compelled  to  use  other  means 
to  restore  to  the  same  its  original  tension. 
The  simplest  and  most  effective  way 
of  attaining  this  end  is  by  re-filling  the 
rims  of  the  wheels,  i.e.,  by  increasing 
their  respective  diameters  to  the  proper 
amount,  which  is  done  in  the  following 
manner.  (See  Figs.  40-43.)  Fig.  40 
shows  the  cross  section  of  a  wheel  with 
leather  filling,  and  Fig.  41  the  same 
wheel  with  its  diameter  enlarged  by  the 
superposition  of  the  new  filling,  which  is 
best  made  of  poplar  or  willow-wood.  It 
is  made  by  taking  straight  pieces  of 
about  Ij  inches  in  thickness,  planing 
them  into  the  necessary  shape  to  fit  the 
rim  of  the  wheel,  or  merely  cutting  them 
into  that  shape  by  means  of  a  circular 
saw,  and  providing  their  upper  surfaces 
with  grooves  for  the  ropes.  These  pieces 
are  made  from  45-70  inches  in  length} 
and  are  provided  on  their  in  sides  with 
saw  cuts  going  half-way  through  the 
wood.  When  we  wish  to  put  on  this 
filling,  the  pieces  are  steeped  in  water 


99 

for  a  day  or  two,  to  render  them  more 
flexible.  They  are  then  nailed  to  the 
leather  filling  by  means  of  suitable 
wrought  nails,  which  should  be  some- 
what longer  than  the  thickness  of  both 
fillings  together,  so  that  after  passing 
through  the  leather  they  may  strike  the 
iron  below  and  be  clinched,  thus  afford- 
ing a  better  hold.  The  nails  must  be 
driven  as  shown  in  Figs.  41  and  42,  and 
especial  care  must  be  taken  that  there 
are  no  projecting  ends  within  reach  of 
the  rope.  The  whole  operation  can 
easily  be  performed  in  an  hour,  without 
throwing  off  the  rope.  In  case  the  fill- 
ing of  one  wheel  in  this  manner  is  not 
sufficient  to  accomplish  the  desired 
result,  we  perform  the  same  operation 
on  the  other  wheel.  If  this  is  still  in- 
sufficient, the  whole  process  is  repeated 
with  a  second  layer.  When  the  rope 
has  finally  become  of  a  constant  length, 
which  usually  takes  place  in  the  course 
of  a  year,  we  may  carefully  remove  all 
but  the  leather  filling,  and  then  shorten 
the  rope  to  the  proper  length,  allowing 


100 


it  to  run  on  the  original  filling.  After 
this  treatment,  there  is  usually  no  more 
trouble  to  be  apprehended  from  this 


102 

source,  but  there  are  some  other  difficul- 
ties which  must  be  guarded  against. 

When  the  transmission  is  in  good  run- 
ning order,  the  ropes  should  run  very 
steadily  and  without  swaying  laterally. 
If  the  latter  does  occur,  it  is  due  to  one 
or  more  of  the  following  causes,  (leaving 
out  of  consideration  the  slight  swaying 
motion  produced  by  the  wind,  or  by  an 
excessive  velocity) ; 

1.  When  the  wheels  are  not  perfectly 
balanced  or  are  not  true  circles. 

2.  When  the  wheels  are  not  in   the 
proper  plane. 

3.  When  the  filling  is  in  bad   condi- 
tion. 

4.  When  the  rope  is  too  much  worn. 

5.  If  the  rope  has  been  badly  spliced. 

6.  If  the  rope  touches  the  ground  or 
other  obstructions. 

I/  It  is  absolutely  necessary  to  balance 
the  wheels  perfectly;  as,  if  they  are  not 
well  balanced,  the  centrifugal  force,  at 
the  velocity  with  which  they  are  diiven, 
exercises  a  very  prejudicial  effect  on  the 
bearings  of  the  shaft,  as  well  as  on  the 


103 

rope.  The  bearings  wear  out  faster  and 
waste  more  power  in  useless  friction, 
while  the  rope  begins  to  swing,  some- 
times to  such  an  extent  as  to  be  thrown 
violently  against  the  side  of  the  wheel 
groove  thus  wearing  out  very  rapidly. 

2/  In  mounting  a>  transmission,  the 
greatest  care  should  be  taken  to  get  the 
wheels  in  the  same  vertical  plane,  and 
the  shafts  perfectly  horizontal,  inasmuch 
as  any  deviation  from  this  position  im- 
mediately shows  itself  in  the  rope. 

3/  In  case  the  filling  is  in  bad  condi- 
tion and  worn  unequally,  it  causes  the 
rope  to  swing  in  a  vertical  plane.  The 
remedy  is  to  cut  the  filling  so  as  to  make 
it  equally  thick  all  around. 

4/  If  there  are  ends  of  wires  project- 
ing from  the  rope,  then  every  time  that 
one  of  these  projections  passes  over  the 
wheel,  the  rope  receives  a  slight  shock, 
causing  it  to  swing.  The  same  action 
takes  place  if  torn  or  loose  strands  occur 
in  the  rope. 

5/  If  the  rope  has  been  badly  spliced, 
or  given  a  false  turn,  it  will  not  run 
steadily. 


105 

6/  When  the  rope  has  stretched  to 
such  an  extent  as  to  touch  the  ground  or 
other  obstructions,  it  begins  to  swing 
violently.  An  attempt  has  sometimes 
been  made  to  remedy  this  by  putting  in 
a  little  roller  or  guide,  which,  however, 
usually  makes  matters  worse. 

There  are  some  other  causes  which 
induce  an  irregular  action  in  the  rope. 
For  instance,  if  a  wire  rope  is  transmit- 
ting a  constant  power  to  a  certain  dis- 
tance, and  if  the  wheels,  ropes,  etc.,  are 
in  good  order,  it  will  run  steadily  as  long 
as  the  power  transmitted  corresponds  to 
a  certain  tension  and  deflection  in  the 
rope.  But  now,  if  some  of  the  machines 
are  suddenly  thrown  in  or  out  of  gear, 
the  tension  in  the  rope  and  its  corre- 
sponding deflection  will  be  changed,  thus 
causing  the  rope  to  sway  gently  in  a 
vertical  plane.  The  result  is,  of  course, 
that  the  motor  will  change  its  speed  to 
suit  the  new  demand  for  power.  This 
property  is  of  great  value,  particularly 
in  long  transmissions,  as  it  prevents  sud- 
den changes  in  velocity,  the  rope  itself 
acting  as  a  sort  of  governor. 


106 


Another  cause  of  swinging  is  found  in 
very  powerful  transmissions,  where  it 
becomes  necessary  to  use  two  ropes  to 
transmit  the  power,  connecting  the  two 
wheels  by  a  differential  gear.  The  ob- 
ject of  this  gear  is  to  equalize  the  tension 


in  the  two  ropes,  as  neither  this  nor  the 
diameter  of  the  wheel  can  be  exactly 
maintained  in  two  wheels  running  side 
by  side.  As  the  cross-head  of  the  differ- 
ential gear  is  firmly  connected  with  the 
shaft,  while  the  wheels  with  their  bevel- 


107 

gear  run  loose  on  the  same,  the  result  is 
that  when  the  tensions  or  the  effective 
diameters  of  the  wheels  are  not  the  same 
in  both,  there  is  an  additional  rotation 
of  one  or  the  other,  caused  by  the  differ- 


ential gear.  This  produces  slight  verti- 
cal oscillations,  which,  however,  have  no 
prejudicial  influence  on  the  working  of 
the  ropes. 

Wire   ropes    are   sometimes    used   to 


transmit  the  power  of  a  steam-engine  to 
a   distant   building,   or    to    combine   its 


109 

power  with  that  of  some  hydraulic  mo- 
tor. In  such  cases,  we  must  be  very 
sure  of  the  regular  action  of  the  steam- 
engine;  as  it  often  happens,  particularly 
in  the  case  of  an  expanding,  single  cylin- 
der engine,  with  a  light  or  badly  bal- 
anced fly-wheel,  that  the  speed  during  a 
stroke  is  irregular.  If  we  attempt  to 
transmit  the  power  of  such  an  engine 
by  means  of  wire  ropes,  the  result  will 
be  a  series  of  oscillations  in  the  latter,  in 
synchronism  with  the  stroke  of  the  en- 
gine. When  this  occurs,  it  can  only  be 
remedied  by  using  a  heavier  and  better 
balanced  fly-wheel,  or  by  adding  a 
second  cylinder  to  the  engine.  These 
irregularities  come  under  the  heading 
(1),  because  the  effect  of  a  badly  bal- 
anced fly-wheel,  is  identical  with  that  of 
a  badly  balanced  driving  wheel.  When 
a  rope  is  used  in  connection  with  a  steam 
engine,  the  latter  wants  a  very  powerful, 
quick-acting  governor,  in  order  to  pre- 
vent the  overrunning  of  the  engine,  if 
the  rope  should  suddenly  break.  Such 
an  accident  happened  a  few  years  ago  in 


110 


a  cotton  spinning  establishment  in 
Alsace,  causing  the  complete  destruction 
of  a  large  steam  engine. 


SECTION  XL 

FILLING   FOR    THE    WHEELS. 

The  filling  first  employed  by  Mr.  A. 
Him,  consisted  of  a  strong  leather  belt, 
covering  the  whole  rim  and  fastened  to 
the  same  by  wooden  wedges.  With 
wheels  of  large  diameter,  he  was  ob- 
liged to  make  this  belt  of  several  pieces, 


Ill 

thereby  weakening  it  considerably.  This 
style  of  filling,  however,  rarely  lasted 
longer  than  a  few  months.  Hirn  was 
then  induced  to  try  rubber,  which  has 
remained  in  considerable  use  up  to  the 
present  day.  But  with  very  large  wheels, 
the  rubber  was  found  to  be  unsuitable 


for  the  following  reasons:  Rubber  ex- 
pands greatly  with  heat,  and  when 
wheels  filled  with  it  are  exposed  to  the 
direct  and  strong  rays  of  the  sun,  the 
rubber  becomes  soft  and  is  cut  by  the 
rope,  or  it  expands  over  the  edge  of  the 
wheel,  causing  the  rope  to  be  thrown  off. 
In  some  cases,  where  the  filling  expanded 


112 


greatly  at  noon,  it  returned  to  its  origi- 
nal position  during  the  night.     On  the 


113 

other  hand,  there  are  cases  known,  when 
in  cold  nights  during  the  stoppage  of 
the  transmission,  the  rope  would  freeze 
to  the  rubber  filling.  On  starting  in  the 
morning,  large  fragments  of  the  brittle 
rubber  were  torn  out.  Besides  this, 
rubber  is  also  slowly  dissolved  by  the  oil 
and  grease  on  the  rope. 

After  some  unsuccessful  attempts  at 
filling  with  hippopotamus  skin,  willow  and 
poplar  wood  were  tried,  giving  quite 
passable  results.  Strips  of  poplar  wood 
about  J  inch  thick  and  seven  to  ten  feet 
long  were  planed  to  the  proper  section, 
softened  in  hot  water,  and  then  driven 
in  without  any  special  fastening.  This 
process  was  very  simple,  allowing  the 
wheels  to  be  re-filled  quickly  and  at 
slight  expense.  The  main  difficulty  was 
that  the  filling  sometimes  became  loose, 
owing  to  the  drying  and  shrinking  of 
the  wood  during  the  hot  season.  This 
was  partly  prevented  by  driving  pieces 
of  wire  through  the  filling  and  the  rim 
of  the  wheel.  The  wood  was  also  soften- 
ed in  hot  glycerine  instead  of  hot  water, 


114 

thus  rendering  it  less  subject  to  the  action 
of  the  air.  In  spite  of  these  precautions, 
a  wooden  filling  rarely  lasted  more  than 
six  or  nine  months,  when  the  wood  was 
most  carefully  selected;  while  if  knots 
or  unsound  spots  were  present  in  the 
filling,  it  wore  out  in  a  still  shorter 
period.  Various  other  woods  were  then 
tried,  but  willow  and  poplar  were  found 
to  be  the  most  durable  as  well  as  the 
cheapest.  As  wood  wears  less  when 
subjected  to  strain  and  pressure  across 
the  direction  of  the  grain,  this  method 
was  also  tried,  notably  at  the  immense 
Schaffhausen  water  works.  In  this  case, 
small  pieces  were  cut,  having  the  fibre 
running  from  side  to  side  of  the  rim  of 
the  wheel.  These  pieces  were  then  dried 
thoroughly,  and  frequently  immersed  in 
linseed  varnish  until  they  were  complete- 
ly saturated  with  the  latter,  thus  becom- 
ing more  durable  and  air-tight.  Not- 
withstanding these  precautions,  some  of 
the  pieces  became  loose,  and,  although 
more  durable  than  the  plain  wood  filling 
previously  described,  they  did  not  last 


115 

longer  than  about  one  year.  A  farther 
trial  was  made  with  wood  filling,  in 
which  the  fibres  ran  radially,  but  with 
no  better  results.  But  this  last  method 
has  the  advantage  that  when  the  rope 
wears  a  groove  into  the  wood,  the  sides 
do  not  split  off  as  easily  as  in  the  two 
other  styles.  Cork  has  also  been  tried 
to  some  extent,  but  it  was  found  of  little 
value  to  transmit  any  considerable  force, 
as  it  wore  out  very  rapidly. 

Again,  by  wedging  the  groove  full  of 
tarred  oakum,  a  cheap  filling  is  obtained, 
nearly  as  good  as  leather,  and  not  so 
tedious  to  insert. 

Another  plan  is  to  revolve  the  wheel 
slowly,  and  let  a  lot  of  small  sized  ratlin 
or  jute-yarns  wind  up  on  themselves  in 
the  groove;  then  secure  the  ends.  After 
a  day  or  two  of  running,  the  pressure  of 
the  rope,  together  with  the  tar,  will  have 
made  the  filling  compact. 

The  first  attempts  with  the  radial 
leather  filling  were  made  about  1865; 
and  it  was  soon  found  that  this  method 
of  filling  was  so  decidedly  superior  to  all 


116 

others,  that  it  has  now  come  into  almost 
exclusive  use.  It  is  easily  inserted  by 
any  ordinary  mechanic.  The  separate 
pieces  of  leather  are  driven  hard  against 
each  other  in  the  groove  of  the  wheel. 
The  key  or  closing  piece  is  made  of  india- 
rubber,  which  is  first  softened  in  hot 
water  and  then  driven  into  its  proper 
place.  The  greatest  wear  of  the  filling 
occurs  not,  as  might  be  expected,  in  the 
driving  wheels,  but  in  the  carrying 
sheaves  of  an  intermediate  station,  and 
there  principally  in  the  smaller  pulley. 
This  is  due  partly  to  the  great  speed,  and 
partly  to  the  fact  that  the  perimetral 
velocity  of  the  pulley  is  often  greater 
than  that  of  the  rope  itself. 

The  life  of  leather  filling  depends  on 
the  quality  of  leather  used,  and  on  the 
radial  thickness  of  the  pieces.  It  is  also 
affected  by  the  tension,  and  .general  con- 
dition of  the  ropes.  It  may  usually 
be  estimated  at  about  three  years. 

SECTION  XII. 

EFFICIENCY. 

The  losses  in  the  transmission  of  power 


117 

by  wire  ropes  are  caused  by  several  re- 
sistances: 

1.  The  rigidity  of   the  wire  ropes  in 
circumflexure  of  the  two  main  wheels, 
and    through    the    change    of    angular 
direction  at  either  side  of  the  carrying 
sheaves. 

2.  Friction  of  shafts  of  the  wheel. 

3.  Resistance  of  the  air  to  the  rotation 
of  the  wheels  and  to  the  passage  of  the 
rope  through  it. 

The  loss  due  to  the  rigidity  of  the 
ropes  may  be  regarded  as  insensible; 
because  when  the  diameters  of  the  pul- 
leys are  sufficiently  large,(  the  wires  of 
which  the  rope  is  made  straighten  them- 
selves by  their  own  elasticity  after  hav- 
ing been  bent. 

The  losses  due  to  the  friction  of  the 
shafts,  and  the  resistance  of  the  air,  have 
been  determined  theoretically  and  prac- 
tically. Letting,  as  before,  tr—  working 
tension,  £0— tension  produced  by  bend- 
ing, we  have  for  the  loss  of  power  for 
the  two  main  wheels,  when 


118 

f 

t     =   t         i         *        H       a       3* 

loss=:.024     .025     .024    .022     .020     .016 
The   greatest   loss    .025   takes    place 

when  r— i>  as  might  have  been  expected; 

*• 
for  we  previously  found  this  to  be  the 

condition  for  obtaining  the  smallest 
wheel.  But  even  this  maximum  loss  is 
a  trifle.  If  we  consider,  that  with  favor- 
able conditions,  we  can  lead  a  wire  rope 
from  500-900  feet  without  any  interme- 
diate support,  while  shafting  of  this 
length  would  cost  an  immense  sum, 
besides  being  exceedingly  inefficient,  we 
can  well  appreciate  the  convenience  and 
value  of  this  method  of  transmitting 
power. 

For  the  carrying  sheaves  the  loss  is  as 
follows:  when 

1  f  I*         2         3* 

l» 
loss= 

.0012  .0013  .0012  .0011   .0010  .0080 

So  that  the  efficiency  in  the  most  un- 

•   t' 
favorable  circumstances,  i.e.  when  j=^ 

may  be  arrived  at  thus : 


119 

1.  Overcoming  the  axle  friction  of 
the  driving  and  following  main- 
pulleys , 0.250 

2.  Overcoming  axle  friction  of  each 
intermediate  sheave 0013 

Hence  the  efficiency  is  E=.975 — .0013 
N,  where  N  is  the  number  of  carrying 
sheaves. 

SECTION  XIII. 

ESTIMATES. 

It  is  impossible  to  give  any  definite 
idea  as  to  the  cost  of  erecting  and  main- 
taining a  transmission.  In  France,  where 
by  far  the  greater  number  of  applications 
are  made,  the  cost  of  the  machinery  and 
its  erection  is  estimated  at  5,000  francs 
per  kilometer,  exclusive  of  the  necessary 
constructions  at  the  termini,  which  are 
said  to  require  an  additional  expenditure 
of  twenty-five  francs  per  horse  power. 

The  average  cost  is  about  one-fifth 
that  of  belting,  and  about  one-twenty- 
fifth  that  of  shafting. 

But  the  number  of  carrying  sheaves, 


120 

distance,  height  of  columns,  etc.,  vary 
so  exceedingly,  that  no  more  than  a  very 
vague  idea  can  be  given  of  the  cost  ex- 
cept by  making  an  estimate  for  every 
special  case.  To  make  this  a  matter  of 
ease,  I  have  appended  a  list  of  the  cur- 
rent prices  of  several  articles,  the  first 
being  the  price  of  "  Wheels  bored  to  fit 
shaft  and  lined  with  rubber  or  leather": 
Diameter.  Price. 

1*  feet $6.00each. 

2  "  8.00     " 

3  " 25.00     " 

4  "  33.00     " 

5  "  53.00     " 

ft       "  75.00     " 

7  "  95.00  " 

8  "  125.00  " 

9  "  cast  in  halves       225.00  **  : 

10  " 300.00  " 

11  "  350.00  " 

12  M  400.00  " 

Special  prices  for  larger  wheels. 

When  the  lining  is  worn  out  in  these 
wheels,  new  filling,  either  of  rubber  or 
leather  may  be  bought  at  60  cents  per 
pound. 

The  price  of  the  ropes  will  be  found  in 
the  wire-rope  table  previously  given. 


121 
SECTION  XIV. 

HISTORICAL    SKETCH. 

The  first  transmission  was  put  up  by 
the  brothers  Him  in  1850,  at  a  calico 
weaving  establishment,  near  Colmar. 
An  immense  mass  of  scattered  build- 
ings seemed  to  forbid  the  possibility  of 
using  them,  and  yet  placing  the  motive  - 
power  at  any  one  point.  In  this  emer- 
gency, they  first  tried  this  method  of 
force  transmission,  using  a  riveted  steel 
ribbon  to  each  building  from  the  engine- 
house.  The  steel  bands  were  about  2  J 
inches  wide  ^v  ^  of  an  inch  thick,  and 
ran  on  wood-faced  drums.  This  pre- 
sented two  inconveniences.  In  the  first 
place,  on  account  of  its  considerable  sur- 
face, the  band  was  liable  to  be  agitated 
by  the  wind;  and  secondly,  it  soon 
became  worn  and  injured  at  the  points 
where  it  was  riveted.  It  served,  however, 
very  well  for  eighteen  months  to  trans- 
mit twelve  horse-power  to  a  distance  of 
eighty  meters. — The  success  of  the*prin- 
ciple  was  complete,  but  much  remained 


122 

to  be  done  before  the  wire  rope  and  the 
rubber  or  leather-lined  driving  wheel 
solved  all  difficulty,  and  brought  the 
principle  to  be  a  practical  reality. 

The  number  of  applications  of  this 
method  of  transmitting  power  has  in- 
creased very  rapidly.  At  the  end  of 
1859,  there  were  but  few  applications  in 
use.  In  1862,  there  are  known  to  have 
been  about  400,  and  in  186*7  about  800. 
At  the  present  time  there  are  several 
thousand  in  successful  operation.  In 
1864,  a  terrible  explosion  destroyed  al- 
most all  of  the  great  powder  mill  at 
Ockhta,  situated  about  six  miles  from  St. 
Petersburg.  The  whole  establishment 
was  rebuilt.  After  studying  many  com- 
binations, an  artillery  officer  proposed  to 
profit  by  the  resources  which  the  telo- 
dynamic  cables  offered  to  engineers,  and 
thus  to  realize  the  only  combination 
which  could  prove  snccessful  in  a  pow- 
der-mill; namely,  a  great  distance  be- 
tween the  buildings,  so  that  the  explosion 
of  one  should  not  entail  the  ruin  of  the 
rest.  The  new  establishment,  which 


123 

went  into  operation  in  1867,  is  composed 
of  thirty-four  different  workshops  or 
laboratories,  to  which  motive  power  is 
transmitted  by  means  of  wire  ropes 
driven  by  three  turbines,  thus  distrib- 
uting a  total  of  274  horse-power  along  a 
line  nearly  a  mile  in  length. 

The  largest  transmission  is  that  em- 
ployed to  utilize  the  falls  of  the  Rhine, 
near  Schaffhausen,  in  Switzerland.  Ad- 
vantage was  taken  of  the  rapids  at  one 
side,  to  put  in  a  number  of  turbines, 
aggregating  in  all  600  horse-power. 
Since  the  steep  rocky  banks  forbade  the 
erection  of  any  factories  in  the  imme- 
diate vicinity,  the  entire  power  was 
transferred  diagonally  across  the  stream 
to  the  town,  about  a  mile  further  down, 
and  there  distributed,  certain  rocks  in 
the  water  being  made  use  of  to  set  up  the 
required  intermediate  stations.  In  the 
industries  we  frequently  meet  with  a 
similar  case.  Many  valuable  sites  for 
water-power  are  lying  idle  in  this  coun- 
try, for  want  of  building  room  in  their 
immediate  vicinity.  New  England  espe- 


124 

cially  abounds  with  them.  Coal  being 
so  dear  there,  their  value  is  all  the 
greater.  Since  the  water  can  only  be 
led  down  hill  in  certain  directions,  the 
cost  of  a  canal  or  flume  would  in  most 
cases  come  too  high,  and  so  the  power 
remains  unimproved.  By  ropes,  how- 
ever, we  can  convey  the  power  of  a  tur- 
bine or  water-wheel  in  any  direction, 
both  up  stream  and  down  stream ;  up  an 
ascent  of  1  in  8  or  10,  or  down  a  moder- 
ate slope  as  well.  The  power  need  not 
be  confined  to  one  factory,  but  may  be 
distributed  among  a  dozen,  if  necessary, 
located  so  as  to  suit  their  particular 
business,  and  not  to  suit  the  oftentimes 
inconvenient  location  of  a  canal. 

Thus,  by  means  of  the  transmission  of 
power  by  wire  ropes,  we  may  utilize  all 
this  power  that  is  now  being  wasted,  and 
devote  it  to  a  useful  purpose. 


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VAN  BUREN.  Investigations  of  Formulas,  for  the 
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JOYNSON.     Designing  and  Construction  of  Machine 

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GILLMORE.  Coignet  Beton  and  other  Artificial  Stone. 
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SAELTZER.  Treatise  on  Acoustics  in  connection  with 
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BUTLER  (W.  F.)    Ventilation  of  Buildings.     By  W.  F. 

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BOW.  A  Treatise  on  Bracing,  with  its  application  to 
Bridges  and  other  Structures  of  Wood  or  Iron.  By 
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cloth i  5o 

BARBA  (J.)  The  Use  of  Steel  for  Constructive  Pur- 
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C.  E      i  ^mo,  cloth i  50 

3 


D.   TAN   NOSTBAND  S   PUBLICATIONS. 


GILLMORE  (Gen.  Q.  A.)  Treatise  on  Limes,  Hy- 
draulic Cements,  and  Mortars.  Papers  on  Practical 
Engineering,  U.  S.  Engineer  Department,  No.  9, 
containing  Reports  of  numerous  Experiments  con- 
ducted in  New  York  City,  during  the  years  1858  to 
1861,  inclusive.  By  Q.  A.  Gillmore,  Bvt.  Maj  -Gen., 
U.  S.  A.,  Major,  Corps  of  Engineers.  With  num- 
erous illustrations,  i  vol,  8vo,  cloth  ...............  $4  oo 

HARRISON.  The  Mechanic's  Tool  Book,  with  Prac- 
tical Rules  and  Suggestions  for  Use  of  Machinists, 
Iron  Workers,  and  others.  By  W.  B.  Harrison, 
associate  editor  of  the  "  American  Artisan."  Illus- 
trated with  44  engravings,  izmo,  cloth  ............  i  50 

HENRICI  (Glaus).  Skeleton  Structures,  especially  in 
their  application  to  the  Building  of  Steel  and  Iron 
Bridges.  By  Olaus  Henrici.  With  folding  plates 
and  diagrams,  i  vol.  Svo,  cloth  ...................  i  50 

HEWaON  (Wm.)  Principles  and  Practice  of  Embank 
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vees of  the  Mississippi.  By  William  Hewson,  Civil 
Engineer,  i  vol.  Svo,  cloth  .......................  2  oo 

HOLLEY  (A.  L.)  Railway  Practice.  American  and 
European  Railway  Practice,  in  the  economical  Gen- 
eration of  Stearc,  including  the  'Materials  and  Con- 
struction of  Coal-burning  Boilers,  Combustion,  the 
Variable  Blast,  Vaporization,  Circulation,  Superheat- 
ing, Supplying  and  Heating  Feed-water,  etc.,  and 
the  Adaptation  of  Wood  and  Coke-burning  Engines 
to  Coal-burning  ;  and  in  Permanent  Way,  including 
Road-bed,  Sleepers,  Rails,  Joint-fastenings,  Street 
Railways,  etc.,  etc.  By  Alexander  L.  Holley,  B.  P. 
With  77  lithographed  plates,  i  vol.  folio,  cloth  ----  12  oo 

KING  (W.  H.)  Lessons  and  Practical  Notes  on  Steam, 
the  Steam  Engine,  Propellers,  etc.,  etc.,  for  Young 
Marine  Engineers,  Students,  and  others.  Bv  the 
late  W.  H.  King,  U.  S.  Navy.  Revised  by  Chief 
Engineer  J.  W.  King,  U-  S.  Navy.  Nineteenth  edi- 
tion, enlarged.  8ro,  cloth  ........................  2  oo 

M[NIME(Wm.)  Mechanical  .Drawing  A  Text-Book 
of  Geometrical  Drawing  for  the  use  of  Mechanics 


J_.    VAN   NOSTBANDS   PUBLICATIONS. 

an&  Schools,  in  which  the  Definitions  and  Rules  ot 
Geometry  are  familiarly  explained;  the  Practical 
Problems  are  arranged,  from  the  most  simple  to  the 
more  complex,  and  in  their  description  technicalities 
are  avoided  as  much  as  possible.  With  illustrations 
for  Drawing  Plans,  Sections,  and  Elevations  of  Build- 
ings and  Machinery;  an  Introduction  to  Isometrical 
Drawing,  and  an  Essay  on  Linear  Perspective  and 
Shadows.  Illustrated  with  over  ?oo  diagrams  en- 
graved on  steel.  By  ^m.  Minifie,  Architect.  Ninth 
edition.  With  an  Appendix  on  the  Theory  and  Ap- 
plication of  *  olors.  i  vol.  8vo,  cloth $4  oo 

"It  Is  the  best  work   on  Drawing  that  we  have  ever  seen,  and  is 

•specially  a  text-book  of  Geometrical  Drawing  tor  the  use  ot  Mechanics 

«vl  Schools.    No  young  Mechanic,  such  as  a  Machinists,  Engineer,  Oabi- 

st-maker,   Millwright,  or    Carpenter,  should  be  without  it."— Srienttfe 


Geometrical  Drawing.  Abridged  from  the  octavo 

»  edition,  for  the  use  of  Schools.  Illustrated  with  48 
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STILLMAN  (Paul.)  Steam  Engine  Indicator,  and  the 
Improved  Manometer  Steam  and  Vacuum  Gauges — 
their  Utility  and  Application.  By  Paul  Stillman. 
New  edition,  i  vol.  i2mo,  flexible  cloth i  ow 

SWEET  (S.  H.)  Special  Report  on  Coal ;  showing  its 
Distribution,  Classification,  and  cost  delivered  over 
different  routes  to  various  points  in  the  State  of  New 
York,  and  the  principal  cities' on  the  Atlantic  Coast. 
By  S.  H.  Sweet.  With  maps,  i  vol.  8vo,  cloth 3  oo 

WALKER  (W.  H.)  Screw  Propulsion.  Notes  on 
Screw  Propulsion  :  its  Rise  and  History.  By  Capt. 
W.  H.  Walker,  U,  S.  Navy,  i  vol.  8vo,  cloth 75 

WARD  (J.  H.)  Steam  for  the  Million.  A  popular 
Treatise  on  Steam  and  its  Application  to  the  Useful 
Arts,  especially  to  Navigation.  By  ].  H.  Ward, 
Commander  U.  S.  Navy.  New  and  revised  edition, 
i  vol.  Svo,  cloth i  oo 

WIESBACH  (Julius).  A  Manual  of  Theoretical  Me- 
chanics. By  Julius  Weisbach,  Ph.  D.  Translated 
from  the  fourth  augmented  and  improved  German 
edition,  with  an  Introduction  to  the  Calculus,  by  Eck- 
ley  B.  Coxe,  A.  M.,  Mining  Engineer.  1,100  pages, 
and  902  wood-cut  illustrations.  Svo,  cloth 1000 

5 


D.  VAN  NOSTBAND'S  PUBLICATIONS. 

DIEDRICH.  The  Theory  <-f  Strains,  a  Compendium 
for  the  calculation  and  construction  of  Bridges,  Hoofs, 
and  Cranes,  with  the  application  of  Trigonometrical 
>  otes,  containing  the  most  comprehensive  informa- 
tion in  regard  to  the  Resulting  strains  for  a  perman- 
ent Load,  as  also  for  a  combined  (Permanent  and 
Rolling)  Load  In  two  sections,  adadted  to  the  re- 
quirements of  the  present  time.  By  John  D'edrich, 
C.  E.  Illustrated  by  numerous  plates  and  diagrams. 
Svo,  doth... 5  OQ 

WILLIAMSON  (R.  S.)  On  the  use  of  the  Barometer  on 
Surveys  and  Reconnoissances.  Part  I.  Meteorology 
in  its  Connection  with  Hypsometry.  Part  II.  Baro- 
metric Hypsometry.  By  R,  S.  Wiliamson,  Bvt 
Lieut. -Col.  U.  S.  A.,  Major  Corps  of  Engineers. 
With  Illustrative  Tables  and  Engravings.  Paper 
No.  15,  Professional  Papers,  Corps  of  Engineers, 
i  vol.  410,  cloth i  i  oo 

POOK  (S.  M.)  Method  of  Comparing  the  Lines  and 
Draughting  Vessels  Propelled  by  Sail  or  Steam. 
Including  a  chapter  on  Laying  off  on  the  Mould- 
Loft  Floor.  By  Samuel  M.  Pook,  Naval  "Construc- 
tor, i  voL  Svo,  with  illustrations,  cloth 5  oo 

ALEXANDER  (J.  H.)  Universal  Dictionary  of 
Weights  and  Measures,  Ancient  and  Modern,  re- 
duced to  the  standards  of  the  United  States  of  Ame- 
rica. By  J.  H.  Alexander.  New  edition,  enlarged, 
i  vol.  Svo,  cloth 3  50 

WANKLYN.  A  Practical  Treatise  on  the  Examination 
of  Milk,  and  its  Derivatives,  Cream,  Butter  and 
Cheese.  By  J.  Alfred  Wanklyn,  M.  R.  C.  S.,  i2mc 
cloth i  oo 

RICHARDS'  INDICATOR.  A  Treatise  on  the  Rich 
ards  Steam  Engine  Indicator,  with  an  Appendix  by 
^  W.  Bacon,  M.  E.  iSmo,  flexible,  cloth i  oo 

PORTER  (C.  T.)  A  Treatise  on  the  Richards  Steam 
Engine  Indicator,  and  the  Development  and  Applica- 
tion of  Force  in  the  Steam  Engine.  By  Charles  T. 
Porter.  Third  edition,  revised  and  enlarged.  Svo, 

illustrated,  cloth 3  5° 

4 


IX  VAN  NOSTKAND  S  PUBLICATIONS. 

POPE-  Modern  Practice  of  the  Electric  Telegraph.  A 
Hand  Book  for  Electricians  and  operators.  By  Frank 
L.  Pope  Ninth  edition,  revised  and  enlarged,  and 

fully  illustrated.     8vo,  cloth $2  oo 

«  There  is  no  other  work  oi  this  kind  in  th«  English  language  that  con- 
tains in  80  small  a  compass  so  much  practical  information  in  the  appli- 
cation of  galvanic  electricity  to  telegraphy.  It  should  be  in  the  handaof 
ereryone  interested  in  telegraphy,  or  the  use  of  Batteries  for  other  pur- 
poses." 

EASSIE  (P.  B.)  Wood  and  its  Uses.  A  Hand  Book 
for  the  use  of  Contractors,  Builders,  Architects,  En- 
gineers, and  Timber  Merchants.  By  P.  B.  Eassie. 
Upwards  of  250  illustrations.  8vo,  cloth i  50 

SABINE.  History  and  Progress  of  the  Electric  Tele- 
graph, with  descriptions  of  some  of  the  apparatus. 
By  Robert  Sabine,  C.  E.  Second  edition,  with  ad- 
ditions, 121110,  cloth i  25 

BLAKE.  Ceramic  Art.  A  Report  on  Pottery,  Porce- 
lain, Tiles,  Terra  Cotta  and  Brick.  By  W.  P.  Blake, 
U-  &  Commissioner,  Vienna  Exhibition,  1873.  8vo, 
cloth 2  oo 

BENET.  Electro-Ballistic  Machines,  and  the  Schultz 
Chronoscope.  By  Lieut -Col.  S.  V.  Benet,  Captain 
of  Ordnance,  U.  S.  Army.  Illustrated,  second  edi- 
tion, 4to,  cloth 3  oo 

MICHAELIS.  The  Le  Boulenge  Chronograph,  with 
three  Lithograph  folding  plates  of  illustrations.  By 
Brevet  Captain  O.  E.  Michaelis,  First  Lieutenant 
Ordnance  Corps,  U.  S .  Army,  4to,  cloth 3  oo 

ENGINEERING  FACTS  AND  FIGURES  An 
Annual  Register  of  Progress  in  Mechanical  Engineer- 
ing and  Construction,  for  the  years  1863,  64,  65,  66 
67,  68.  Fully  illustrated,  6  vols.  i8mo,  cloth,  $2.50 
per  vol.,  each  volume  sold  separately 

HAMILTON.  Useful  Information  for  Railway  Men. 
Compiled  by  W.  G.  Hamilton,  Engineer.  Sixth  edi- 
tion, revised  and  enlarged,  562  pages  Pocket  form. 
Morocco,  gilt 2  oo 

STUART  (B.)  How  to  Become  a  Successful  Engineer. 
Being  Hints  to  Youths  intending  to  adopt  the  Pro- 
fession. Sixth  edition,  i  amo,  boards 50 


D.  VAN  N08TRAND  S  PUBLICATIONS. 

STUART.  The  Civil  and  Military  Engineers  of  Amer 
ica.  By  Gen.  C.  B.  Stuart.  With  9  finely  executed 
portraits  of  eminent  engineers,  and  illustrated  by 
engravings  of  some  of  the  most  important  works  con- 
structed in  America-  8vo,  cloth $5  oo 

STONEY.  The  Theory  of  Strains  in  Girders  and  simi- 
lar structures,  with  observations  on  the  application  of 
Theory  to  Practice,  and  Tables  of  Strength  and  other 
properties  of  Materials.  By  Bindon  B.  Stoney,  B.  A. 
New  and  revised  edition,  enlarged,  with  numerous 
engravings  on  wood,  by  Oldham.  Royal  8vo,  664 
pages.  Complete  in  one  volume-  8vo,  cloth 12  50 

SHREVE.  A  Treatise  on  the  Strength  of  Bridges  and 
Roofs.  Comprising  the  determination  of  Algebraic 
formulas  for  strains  in  Horizontal,  Inclined  or  Rafter, 
Triangular,  Bowstring,  Lenticular  and  other  Trusses, 
from  fixed  and  moving  loads,  with  practical  applica- 
tions and  examples,  for  the  use  of  Students  and  Engi- 
neers. By  Samuel  H.  Shreve,  A.  M.,  Civil  Engineer. 
87  wood-cut  illustrations,  ad  edition.  8vo,  cloth ...  5  oo 

MERRILL.  Iron  Truss  Bridges  for  Railroads.  The 
method  of  calculating  strains  in  Trusses,  with  a  care- 
ful comparison  of  the  most  prominent  Trusses,  in 
reference  to  economy  in  combination,  etc.,  etc  By 
Brevet  Col.  William  E.  Merrill,  U  S.  A.,  Major 
Corps  of  Engineers,  with  nine  lithographed  plates  of 
Illustrations.  410,  cloth 500 

WHTPPLE.  An  Elementary  and  Practical  Treatise  on 
Bridge  Building.  An  enlarged  and  improved  edition 
of  the  author's  original  work.  By  S.  Whipple,  C-  E. , 
inventor  of  the  Whipple  Bridges,  &c  illustrated 
8vo,  cloth 4  oo 

THE  KANSAS  CITY  BRIDGE-  With  an  account 
of  the  Regimen  of  the  Missouri  River,  and  a  descrip- 
tion of  the  methods  used  for  Founding  in  that  River. 
ByO  Chanute,  Chief  Engineer,  and  George  Morri- 
son, Assistant  Engineer.  Illustrated  with  five  litho- 
graphic views  and  twelve  plates  of  plans.  410,  cloth,  6*0 

DUBOIS  (A.  J.)  The  New  Method  of  Graphical  Statics. 
By  A.  J  Dubois,  C.  E.,  Ph.  D.  With  60  illustra- 
tions. 8  vo,  cloth .  2  oo 


r>.  v.0^7  SOSTRAND'S  PUBLICATIONS. 


MAC  CORD.  A  Practical  Treatise  on  the  Slide  Valve 
by  Eccentrics,  examining  by  methods  the  action  of  the 
Eccentric  upon  the  Slide  Valve,  and  explaining  the 
Practical  processes  of  laying  out  the  movements, 
adapting  the  valve  for  its  various  duties  in  the  steam 
engine.  For  the  use  of  Engineers,  Draughtsmen, 
Machinists,  and  Students  of  Valve  Motions  in  gene 
ra'..  By  C.  W.  Mac  Cord,  A.  M. ,  Professor  of  Me- 
chanical Drawing,  Stevens'  Institute  of  Technology, 
Hoboken,  N.  J.  Illustrated  by  8  full  page  copper- 
plates. 410.  cloth $3  oo 

K1RKWOOD.  Report  on  ths  Filtration  of  River 
Caters,  for  the  supply  of  cities,  as  practised  in 
Europe,  made  to  the  Board  of  Water  Commissioners 
of  the  City  of  St.  Louis.  By  James  P-  Kirkwood. 
Illustrated  by  30  double  plate  engravings.  4to,  doth,  15  oo 

PLATTNER.  Manual  of  Qualitative  and  Quantitative 
Analysis  with  the  Blow  1'ipe.  From  the  last  German 
edition,  revised  and  enlarged.  By  Prof.  Th.  Richter. 
of  the  Royal  Saxon  Mining  Academy.  Translated 
by  Prof.  H.  B.  Cornwall,  Assistant  in  the  Columbia 
School  of  Mines,  New  York  assisted  by  John  H. 
Caswell.  Illustrated  with  87  wood  cuts,  and  one 
Kthographic  plate.  Third  edition,  revised,  560  pages, 
STO,  cloth 7  50 

PLYMPTON.  The  Blow  Pipe.  A  Guide  to  its  Use 
in  the  Determination  of  Salts  and  Minerals.  Com- 
piled from  various  sources,  by  George  W.  Plympton, 
C  E.  A.  M.,  Professor  of  Physical  Science  in  the 
Polytechnic  Institute,  Brooklyn,  New  York,  jamo, 
cloth i  50 

PYNCHON.  Introduction  to  Chemical  Physics,  design- 
ed for  the  use  of  Academies,  Colleges  and  High 
Schools.  Illustrated  with  numerous  engravings,  and 
containing  copious  experiments  with  directions  for 
preparing  them.  By  Thomas  Ruggles  Pynchon, 
M.  A.,  Professor  of  Chemistry  and  the  Natural  Sci- 
ences, Trinity  College,  Hartford  New  edition,  re- 
vised and  enlarged,  and  illustrated  by  269  illustrations 
onwood.  Crown,  8vo.  clotfe 300 

9 


D.  TAN  NOSTBAND'S  PUBLICATION*. 

ELIOT  AND  STORER.  A  compendious  Manual  of 
Qualitative  Chemical  Analysis.  By  Charles  W. 
Eliot  and  Frank  H.  Storer-  Revised  with  the  Co- 
operation of  the  authors.  By  William  R.  Nichols, 
Professor  of  Chemistry  in  the  Massachusetts  Insti- 
tute of  Technology  Illustrated,  izmo,  doth. $  i  50 

RAMM  ELS  BERG.  Guide  to  a  course  of  Quantitative 
Chemical  Analysis,  especially  of  Minerals  and  Fur- 
nace Products.  Illustrated  by  Examples  By  C.  F- 
Ramroalsberg.  Translated  by  J.  Towler,  M.  D. 
8vo,  cloth 2  23 

DOUGLASS  and  PRESCOTT.  Qualitative  Chemical 
Analysis.  A  Guide  in  the  Practical  Study  of  Chem- 
istry, and  in  the  Work  of  Analysis.  By  S'.  H.  Doug- 
lass and  A.  B.  Prescott,  of  the  University  of  Michi- 
gan. New  edition.  8vo.  In  prets. 

JACOB.  On  the  Designing  and  Construction  of  Storage 
Reservoirs,  with  Tables  and  Wood  Cuts  representing 
Sections,  &c.,  iSmo,  boards 50 

WATT'S  Dictionary  of  Chemistry.  New  and  Revised 
edition  complete  in  6  vols.  8vo  cloth,  $62.00.  Sup- 
plementary volume  sold  separately.  Price,  cloth. . .  9  oo 

RANDALL.  Quartz  Operators  Hand-Book.  By  P.  M. 
Randall.  New  edition,  revised  and  enlarged,  fully 
illustrated.  i2mo»  cloth  200 

SILVERSMITH.  A  Practical  Hand-Book  for  Miners, 
Metallurgists,  and  Assayers,  comprising  the  most  re- 
cent improvements  in  the  disintegration,  amalgama- 
tion, smelting,  and  parting  of  the  Precious  ores,  with 
a  comprehensive  Digest  of  the  Mining  Laws-  Greatly 
augmented,  revised  and  corrected.  By  Julius  Silver- 
smith. Fourth  edition.  Profusely  illustrated.  i2mo, 
doth 3  oo 

THE  USEFUL  METALS  AND  THEIR  ALLOYS, 
including  Mining  Ventilation,  Mining  .Jurisprudence, 
and  Metallurgic  Chemistry  employed  in  the  conver- 
sion of  Iron,  Copper,  Tin,  Zinc,  Antimony  and  Lead 
ores,  with  their  applications  to  the  Industrial  Arts. 
By  Scofiren,  Truan,  Clay,  Oxland,  Fairbairn,  and 

•thers.     Fifth  edition,  half  calf 3  7« 

10 


D.  TAN  NO8TRAND  S  PUBLICATIONS. 

JOYNSON.  The  Metals  used  in  construction,  lion, 
Steel,  Bessemer  Metal,  etc.,  etc.  By  F.  H.  Joynson. 
Illustrated,  i2mo,  cloth $o  75 

VON  GOTTA.  Treatise  on  Ore  Deposits.  By  Bern- 
hard  Von  Cotta,  Professor  of  Geology  in  the  Royal 
School  of  Mines,  Freidberg,  Saxony.  Translated 
from  the  second  German  edition,  by  Frederick 
Prime,  Jr.,  Mining  Engineer,  and  revised  by  the  au- 
thor, with  numerous  illustrations.  8vo,  cloth 4  oo 

GREENE.  Graphical  Method  for  the  Analysis  of  Bridge 
Trusses,  extended  to  continuous  Girders  and  Draw 
Spans.  By  C.  K.  Greene,  A.  M.,  Prof,  of  Civil  Engi- 
neering, University  of  Michigan.  Illustrated  by  3 
folding  plates,  8vo,  cloth a  co 

BELL.  Chemical  Phenomena  of  Iron  Smelting.  An 
experimental  and  practical  examination  of  the  cir- 
cumstances which  determine  the  capacity  of  the  Blast 
Furnace,  The  Temperature  of  the  air,  and  the 
proper  condition  of  the  Materials  to  be  operated 
upon.  By  I.  Lowthian  Bell.  8vo,  cloth 6  •• 

ROGERS.  The  Geology  of  Pennsylvania.  A  Govern- 
ment survey,  with  a  general  view  of  the  Geology  of 
the  United  States,  Essays  on  the  Coal  Formation  and 
its  Fossils,  and  a  description  of  the  Coal  Fields  of 
North  America  and  Great  Britain.  By  Henry  Dar- 
win Rogers,  late  State  Geologist  of  Pennsylvania, 
Splendidly  illustrated  with  Plates  and  Engravings  in 
the  text.  3  vols.,  4to,  cloth,  with  Portfolio  of  Maps.  30  oo 

BURGH.  Modern  Marine  Engineering,  applied  to 
Paddle  and  Screw  Propulsion.  Consisting  of  36 
:olored  plates,  259  Practical  Wood  Cut  Illustrations, 
and  403  pages  ot  descriptive  matter,  the  whole  being 
an  exposition  of  the  present  practice  of  James 
Watt  &  Co.,  J.  &  G.  Rennie,  R.  Napier  &  Sons, 
and  other  celebrated  firms,  by  N.  P.  Burgh,  Engi- 
neer, thick  4to,  vol.,  doth,  $25.00 ;  half  mor. 30  oo 

CHURCH.    Notes  of  a  Metallurgical  Journey  in  Europe. 

By  J.  A.  Church,  Engineer  of  Mines,  8vo,  cloth 2  oo 

11 


D.  TAN  NOSTRANITS  PUBLICATIONS. 
dJ 

BO  CTRNE.  Treatise  on  tht  Steam  Engine  in  its  various 
applications  to  Mines,  Mills,  Steam  Navigation, 
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By  John  Bourne,  being  the  ninth  edition  of  "  A 
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STUART.  The  Naval  Dry  Docks  of  the  United 
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BARNES  Submarine  Warfare,  offensive  and  defensive, 
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JEFFER'S.  Nautical  Surveying.  By  W.  N.  Jeffers, 
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MORFIT.  A  Practical  Treatise  on  Pure  Fertilizers,  and 
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complete  Mathematical,  Astronomical  and  Practical 
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veyors in  the  Field.  By  S.  R.  Clevenger,  Pocket 
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PICKERT  AND  METCALF.  The  Art  of  Graining. 
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LAZELLE.  One  Law  in  Nature.  By  Capt.  H.  M. 
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cal Affections  or  Modes  of  Energy,  izmo,  doth. . .  i  50 

CORFIELD.  Water  and  Water  Supply.  Bv  W  H 
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WOOD.  West  Point  Scrap  Book,  being  a  collection  of 
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WEST  POINT  LIFE.  A  Poem  read  before  the  Dia- 
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HENRY.  Military  Record  of  Civilian  Appointments  in 
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PRESCOTT.  Outlines  of  Proximate  Organic  Analysis, 
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PRESCOTT.  Chemical  Examination  of  Alcoholic  Li- 
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their  Qualitative  and  Quantitative  Determinations. 
By  Albert  B.  Prescott,  i2tno,  cloth 150 

NAQUET.  Legal  Chemistry.  A  Guide  to  the  De- 
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AXON.  The  Mechanics  Friend;  a  Collection  of  Re- 
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ERNST.  Manual  of  Practical  Military  Engineering,  Prt 
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Academy,  and  for  Engineer  Troops.  By  Oapt.  O.  H. 
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Military  Engineering,  U.  S.  Military  Academy.  192 
wood  cuts  and  3  lithographed  plates.  i2mo,  cloth..  500 

BUTLER.  Projectiles  and  Rifled  Cannon.  A  Critical 
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Projectiles,  with  Practical  Suggestions  for  their  Im- 
provement, as  embraced  in  a  Keport  to  the  Chief  of 
Ordnance,  U.  S.  A.  By  Capt.  John  S.  Butler,  Ord- 
nance Corps,  U.  S.  A.  36  plates,  410,  doth 7  50 

BLAKE.  Report  upon  the  Precious  Metals :  Being  Sta- 
tistical Notices  of  the  principal  Gold  and  Silver  pro- 
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Paris  Universal  Exposition.  By  William  P.  Blake, 
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TONER.  Dictionary  of  Elevations  and  Climatic  Regis- 
ter of  the  United  States.  Containing  in  addition  to 
Elevations,  the  Latitude,  Meaif,  Annual  Temperature, 
and  the  total  Annual  Rain  fall  of  many  localities;  with 
a  brief  introduction  on  the  Orographic  and  Physical 
Peculiarities  of  North  America.  By  J.  M.  Toner, 
M.  D.  8vo,  doth 3  75 

MOWBRAY.  Tri-Nitro  Glycerine,  as  applied  in  the 
Hoosac  Tunnel,  and  to  Submarine  Blasting,  Torpe- 
does, Quarrying,  etc.  Being  the  result  of  six  year's 
observation  and  practice  during  the  manufacture  of 
five  hundred  thousand  pounds  of  this  explosive  Mica, 
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various  Systems  of  Blasting  by  Electricity,  Priming 
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tions, tables  and  appendix.  Third  Edition.  Re- 
written, 8vo  doth 3  oc 

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ROBERTS  (Joseph).  Hand-Book  of  Artillery  for  the 
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HAUPT  (Herman).  Military  Bridges,  including  De- 
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AVELING  (S.  T.)    Carpentry  and  Joinery.    A  Useful 

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GRIFFITH  (J.  W.)    An  Elementary  Text-Book  of  the 

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NAPIER  (Jamas).  Manual  of  Electro-Metallurgy,  in- 
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DAVIDSON  (E.  A.)  Practical  Manual  of  House  Paint- 
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WILSON  (Geo.)  Inorganic  Chemistry.  Revised  and 
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BURN  (Robert  Scott).  Ornamental  Drawing  and  Archi- 
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RANKINE  (W.  J.  MACQUORN).  A  Manual  of  Ap- 
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"  Cannot  fail  to  be  adopted  as  a  Text-Book.  .  .  . 
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A  Manual  of  Machinery    and  Millwork.     With 

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difficult  to  award  to  any  book.  It  cannot  fail  to  be  a 
lantern  to  the  feet  of  every  Engineer  "—  The  Engineer. 

A  manual  of  the  Steam  Engine  and  other  Prime 

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Crown  8vo,  cloth 5  oo 

Useful  Rules  and  Tables  for  Architects,  Builders, 

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A  Mechanical  Text-Book  ;  or  introduction  to  the 

Study  of  Mechanics.      By   Professor   Rankine   and 

E.  F.  Bamber.  C.  E.  'Crown  8vo,  cloth 3  50 

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VAN  NOSTRAND'S  SCIEHCE  SERIES. 


A  GRAPHIC  METHOD  FOR  SOLVING  CER- 
TAIN ALGEBRAIC  EQUATIONS.  By  Prof. 
GEORGE  L.  VOSE.  With  Illustrations. 


This  book  is  DUE  on  the  last 
date  stamped  below 


APR2  9 1988 


UC  SOUTHERN  REGIONAL  LIBRARY  FACILITY 


B     000012049     3 


TJ 
1115 


